HA
NGHIA ANH
- NGUYEN THUY
Mtl -
TRAN
KY
TRANH
(Tuyen
chgn
vd
gidi thi$u)
DE
THI TUYEN SINH VAO LdP
10
MON TOAN
OE THI CUA CAC TRl/CfNG CHUYEN, CHQN TREN TOAN QUOC
(Tdi
ban Idn
thiiC
ttC,
c6
8v£a
chUa
bo
sung)
Tm
Vi£N
Tff,'H
EINH THUAN
OWL
f/iiy^e /

Tong
bi&n
tdp: TS.
PHAM
THI
TRAM
Biin
tdp Idn ddu:
NGUYEN
VAN
TRONG
Biin tdp tdi ban:
NGUYEN THUY
Chi ban: NHA
SACH HONG
AN
Trinh
bay bia:
THAI
VAN
B6i tdc Mn ket
xudt
ban:
NHA SACH HONG
AN
SACH LIEN KET
DE
THI
TUYEN
SINH VAO L6P 10 MON TOAN

tC/
nam hpc 2000 den nay.
Chung toi hi vpng cuon sach se rat hufu ich cho cac em tren
con dudng hpc tap.
Trong qua trinh bien soan kho tranh khoi nhufng thieu sot, rat
mong nhan dUpc
S[jl
gdp y cua bgn dpc gan xa.
Chuc cac em thanh cong trong ki thi sap tdi.
CAC TAC GlA
DE
1
TRl/dNC
PnH CHUYEN H6NG PHONG -
TRXN
DAI
NGHTA
L6P CHUY^N
NGUYiN
THl/ONG
HIEN
- L^P
CHUYEN
GIA
DjNH
De thi tuyen
sinh
vao I6p 10
PTTH
chuyen tqi

Giai
cac phiTcfng
trinh
va he phuomg
trinh
:
b) a)
Vs - x^ = X - 1
X y
X y
c) V-x^ + 4x - 2 + V-2x2 + 8x - 5 = V2 + A/3.
Cau
4.
a)
Cho hai so' dirong x, y thoa : x + y =
37xy.
Tinh
—.
y
b)
Tim cac so nguyen dufong x, y thoa : — + i = i.
X y 2
Cau
5, Cho tam gidc ABC c6 ba goc nhon (AB < AC), c6 dudng cao AH. Goi
D,
E Ian
lucrt
1^
trung
diem ciia AB va AC.

A =
V16 + 4V(V5 - 1?1 (Vio -
A/2)
=
(VI6T4(X^(A^
-
5
A
=
(V2A/6
+
2V5)(A/10
-
V2)
=
(A^VCVS
+
1)^
(VlO
- N^)
=
A/2(A/5
+ -
V2)
=
(VlO
+
V2)(VrO
-
V2)

a
+ lj
2(a
-1)
a
+
1
Cau
2.
Phuang
trinh
ho^h dp
giao
dilm
cua (d) (P)
\k
:
o
3x^
+ 6x + 8m = 0
3
o 3 2
— X
+
2m
= —
X
2
4
(*)

hoac
X = 2
X
> 1
2x2
- 2x - 4 = 0
x
= 2.
b)
Dieu ki^n
: x ^ 0, y 0.
Dat
u = i; V = —. H? da cho c6
dang
:
X
y
Vdi
u
= 2, ta c6 : - = 2 => x = i.
X
2
Vdi
V = 1, ta c6 :
—
= 1 => y = 1.
y
So vdi dieu
ki$n
ta

V3
-
2(x
-
2)2
< ^3
Do
do : V-x2 + 4x -
2
+ V-2x2 + 8x - 5 <
+
S
Dau "="
xdy ra o x = 2.
V^y phifcfng
trinh
c6
nghiem
duy
nha't
x = 2.
Cfiu
4.
a)
Ta c6 :
Dat
(1)
x
+ y =
at

X
y 2
x>y>0
=> —<— =>
—
=
—
+
—
<— => y<4.
X
y 2 X y y
Do
do : 2 < y < 4. Ma y la so'
nguyen dUdng
{gik
thiet)
nen y = 3
hoac
y
= 4.
Vdi
y = 3 X = 6. Do
tinh
doi
xuEng
ta
cung
c6 x = 3 va y = 6.
Vdi

•
2- x = -4va 2-y = -l<» x =
6vay
= 3
(nhan)
•
2-x = -2 va 2-y = -2 o x = 4 va y = 4
(nhan).
Vay
ta c6 ckc cap so
nguyen dUdng
(x; y) la : (3; 6), (6; 3), (4; 4).
Cliu
5,
(Hinh
1)
a)
Taco:
DE//BC
nen
HDE
=
BHD.
Tam
giac
vuong
ABH c6 HD la
trung
tuyen
nen DH = DB, suy ra

DE la
tiep tuyen chung
cua
hai
difdng
trbn
ngoai tiep tam
gidc
DBH
va
ECH.
b)
Ta
CO
:
IDF
=
IHD
va
IFD
=
IDH
(=
DBF).
Do
d6 hai
tam
gidc
IDF
va

=
180°; EFH
+
ECH
= 180°.
Trong tam
giac
ABC
c6 :
BAC
+
DBH
+
ECH
= 180°.
^
~ ^ b) 2x2 ^ 2V3^ -3 = 0 c) 9x^ + 8x2 - 1 = 0.
5x + 3y = -4
Lai
CO
:
DFH
+
EFH
+
DFE
=
360°.
Suy
ra

phucfng
trinh
sau :
a)
Cau
2.
Thu
gon cac
bilu
thiJc
sau :
^1-2
Va + 2^ r
_
_ . Va -
-V3'
{yla+2
Va-2j
(vdi
a > 0 vk a 7t 4).
Cau
3. Cho
manh
dat
hinh
chO
nhat
c6
dien
tich

cit
true tung tai diem
c6
tung
dp
bkng
4.
b)
Ve do
thi
hkm so y = 3x + 4 v^ y =
tren
cung
mot he
true
tpa dp.
2
Tim
tpa
dp cac
giac
diem
cua
hai
do
thi
ay
bing
phep
tinh.

AE.AB.
b)
Goi H la
giao
diem ciia BD
va
CE,
goi K la
giac
diem
cua
AH
va B(
ChuTng minh
AH
vuong
goc vdi BC.
c)
TLT
A ke cac
tiep tuyen
AM,
AN
den
dudng
tron
(O) vdi
M,
N la ca
tiep

2V3x-3
= 0 A'= 9 ^ >/A^ = 3.
Phuong
trinh
c6 hai
nghiem phan biet
: x, = ^ ^ •
x.>
= " ^
2
' - 2
c)
9x' + 8x- - 1 =»0.
Dat
t =
X-,
(t > 0).
Phuong
trinh
da cho c6
dang
:
91"
+ 8t - 1 = 0
Vi
a-b + c= l
ti
= -1; tv =
9
So vdi

V^ + 2^
Va+2
Va-2
-aVa a - 4
_
(V^-2)2
^(4a+2f a -4
4a)
(Va+2)(Va-2)
Va
a-4
•
Cau
3. Goi
chieu rong ciia manh
dat luc dau la : x
(m),
(x > 0).
Chieu
dai
manh
dat luc dau la :
360
(m),
Chilu
rong manh dat sau khi tang 2m la : x + 2 (m).
OCA
Chilu
dai manii dat sau khi giani 6m la : 6 (m).
X

-4
-2 0
2
4
-8
-2 0
-2
-8
X
0
-2
y
/
y
= 3x + 4
4
-2
4
Phuong
trinh
hoanh do
giao
diem ciia
2
-4 -2 /
0 2 4
(P) : y = - — va (d) : y = 3x + 4 la :
= 3x + 4 c:> x%6x + 8 = 0
<^ xi = -2 va X2 = -4
Vdi

ABC.
Ma H la
giao
diem ciia BD va CE nen
H
la trirc tam ciia tam
giac
ABC.
Suy ra AH 1 BC.
1
c) Ta CO : ANM = - MON (goc tao bdi
2
Hinh
2
tia
tiep tuyen va day vdi goc d tam ciing
chan
MN).
Ma OA la tia phan
giac
ciia goc MON (tinh
chat
hai tiep tuyen cat
1
nhau) nen AON = - MON, suy ra : AMN = AON
2
(1)
Ta lai c6 : ANO = AMO = 90°, nen
tiif
giac

AN-
=
AH.AK.
AN
AH
AN-
= AE.AB
AE.AB =
AH.AK
3)
(4)
Xet
AANH
va
AANK
c6 : NAK
chung
va ^ ^ .
AK
AN
Suy ra
AANH
or,
AAKN
(c-g-c)
=> ANH = AKN.
Tren ciing mot niia mat phang c6 bd chufa tia
NA,
ta c6 :
ANH

phirong
trinh
: b'"x" + (b'^ + c" - a")x + c" = 0 v6 nghiem.
Cau
2. Giai phifong
trinh
va he phuong
trinh
:
-y^ =3{x^y) 13x
a)
\) — + = 6.
i
X + y = -1 3x- - 5x + 2 3x^ + x + 2
Cau 3.
a)
Chiing
niinh
2(a' + b"*) > ab' + a"b + 2a'b" vdi mpi a, b.
^ b) ChiJng minh Va^ - b" +
V2ab
- b^ > a, vai a > b > 0.
Cau
4. Tim cac so' nguyen diTOng c6 2 chuf so', biet so' do la boi ciia
tich
2
chCf so' ciia chinh so do.
Cau
5. Cho
hinh

+ x,, + m = 0 (*); XQ + mx,, + 1 = 0.
Tirdo (xg+Xo+m)-(x5 + mx„ + 1) = 0 ^ (1 - m)(x„ - 1) = 0.
Voi m = 1, ca hai phUong
trinh
deu c6 dang : x" + x + 1 = 0 (vo nghiem).
Vd-i
x„ = 1 tCr (*) CO m = -2, khi do phuong
trinh
x" + x + m = 0 c6 hai
nghiem la 1 va -2.
PhUong
trinh
x" + mx + 1 = 0 c6 nghiem kep la 1.
Vay m = -2 thi hai phuong
trinh
da cho c6 it nhat mgt nghiem chung.
b) b'-x- + (b- + c'-^ - a^)x + c" = 0
Ja
CO : A = ih- + - a'f - Ah'c' = (b" + c'' - a")" -
(2bc)"
= [(b + c)- - a-ll(b - c)- - a-|
= (b + c + a)(b + c - a)(b - c + a)(b - c - a).
Do a, b, c la do dai ba canh cua tam
giac
nen A < 0.
Vay phaong
trinh
da cho v6 nghiem.
'Cau 2.
x^-y^=3(x-y)

trinh
nen ta chia ve
trai
ciia
phuang
trinh
cho x ta difcfc :
2 13 2 13
, (1; -2), (-2; 1).
3x^ - 5x + 2 3x^ + X + 2
= 6
2 2
3x + 5 3x + - + l
x X
= 6 (*i
Dat y = 3x + - - 5 (*)
dugc
viet lai :
x
- +
-1^
= 6 o 2y''* + 7y - 4 = 0
y
y + 6
Giai phiicfng
trinh
nay ta diTOc : yi = - ; ya = -4-
Vdi
yi = - c=. 3x + - - 5 = i C5. 6x' - llx + 4 = 0 => x, = ^ , - -
2 X 2 3

-b^)(2ab-b^)
>
<^ 2b(a - b) + 2V(a^
-b^)(2ab-b-)
> 0
(dung)
Vay bat dang thiJc da cho dung.
Cau
4. Gpi so can tim la ab (a, b
khac
0). TCf gia thiet c6 ab = m .ab.
Suy ra : 10a + b = mab, hay b = a(mb - 10), suy ra b chia het cho a.
Dat b = na (n < 9).
Tir
na = a(mna - 10) c6 n = mna - 10 o n(ma - 1) = 10 nen chia het
cho n => n e
|1,
2, 5).
- Vdi n = 1 thi ma - 1 = 10 ma = 11, suy ra a = b = 1.
- Vdi n = 2 thi ma - 1 = 5 r=> ma = 6 => a = 1, 2, 3, tUcfng
iifng
c6 b = 2, 4, 6
- Vdi n = 5 thi naa - 1 = 2 <=> ma = 3 => a = 1, tu'Ong
iifng
c6 b = 5.
Thii
lai ta c6 cac so can tim la : 11, 12, 15, 24, 36.
Cau
5. (Hinh 3)
a)

TCf do :
BBjC = ABC, suy ra ABB,C oo
AABC.
BjC BC
BC AC
Hay BC- = AC(AB + AC).
DE
4
Hinh
4
TRl/CfNG
PTTH
CHUYEN
LE HONG PHONG,
TPHCM
De thi tuyen
sinh
vdo I6p 10 (Ban A, B) nam hoc
2005
-
2006
Cau
1. Cho phirong
trinh
(c6 an so la x) : 4x- + 2(3 - 2m)x + m" - 3m +2 = 0.
a)
ChuTng to r&ng phirong
trinh
tren luon c6 nghiem vdi moi gia tri ciia
tham

4. Tim so chinh phuong c6 4 chC so biet rang khi tang them m6i chijf
so mot don vi thi so mdi
dugc
tao thanh cung la mot so chinh phuong.
Cau
5. Cho tam
giac
ABC c6 ba goc nhon noi tiep trong dudng tron (O; R),
so do goc C b^ng 45". Dudng tron dudng
kinh
AB c^t cac canh AC va
BC Ian \mt tai M va N.
AB
a)
Chiifng minh MN vuong goc vdi OC. b) ChiJng minh MN = -j=r.
Cau
6. Cho tam
giac
ABC cd ba goc nhon noi tiep dudng tron (0; R). Diem
M
di
dong
tren
cung'nho
BC. Tii M ke cac difdng th^ng MH, MK Ian
lu'ot
vuong goc vdi AB, AC (H
thuoc
dudng thang AB, K
thuoc

m
—
2
2
— > - —
16 " ~16
Dau "=" xay ra <:5> m =
2
Vay gia tri nho nhat ciia X|.xv la
Cau
2.
a)
. 16
dat duoc khi m
2
x^ + y'^ = 2(xy + 2)
x^ + y^ = 4xy + 4
X + y = 6
<=>
X + y = 6
Giai
ra ta dUdc he c6 hai nghiem (x; y) la : (4; 2), (2; 4).
b) Dieu kien x ^ -5. Phirong
trinh
da cho tuong dirong vdi :
X + y = 6
x.y = 8
X + = 11 <=>
(x + 5f
X -

2
1
+ V2I
X^; =
1
- V2T
2
1-V2I
la hai nghiem ciia phiTcfng
triiih
da cho.
Cau
3.
a)
Ap dung bat d^ng thiifc
Cosi
cho hai so duang, ta c6 :
16
c(a - c)
ab
fc(b - c) _ 17
\b '
V
b
c
''b-c^
[ a J
a
V
b J

Dat n- =
abed
(n E N'). Ta eo n" <
10000
nen n < 100.
Khi
tang m6i
chiJ
so ciia so'
abed
len mot don vi thi dirac so :
(a + l)(b + l)(c + l)(d + l).
Theo
gia thiet (a + l)(b + IKc + l)(d + 1) = m" (m E
N").
Tirong tir nhtf
tren
c6 m < 100.
Suy ra 2 < m + n < 200.
Xet : m- - ir = (a + l)(b + l)(c + l)(d + 1) -
abed
= 1111.
Hay (m - n)(m + n) = 1111.
VI
nil =
1.1111
=
11.101,
nen chi xay ra m - n = 11 va m + n = 101.
suy ra m = 56, n = 45.

(vi
AACN
can tai N)
MN
=
AB
V2'
THLH/IENTI.\!HBINHTHUAN
17
Cau 6.
(Hlnh
6)
a) Bon
diem
A, H, M, K
cung
nkm tren
mot
ducfng
tron
dudng
kinh AM.
Ta CO : MBC = MAC = MHK,
MCB = MAB = MKH.
Suy ra tam
giac
MBC
dong
dang
vdi

HONG
PHONG,
TPHCM
De thi
tuyen
sinh
vao I6p 10 chuyen
Toan
nam hoc
2004
-
2005
Cau 1. Giai he :
2x - y X + y
1
1
2x - y X + y
= -1
= 0
Cau 2. Cho X > 0
thoa
: x" + A- = 7. Tinh x"' + —
Cau 3, Giai phiforng
trinh
:
3x
=
A/3X + 1 - 1.
V3x + 10
Cau 4.

goc vdi MN.
18
b) ChiJng minh : tuT
giac
lOBJ la hhih binh hanh.
c) Chijrng minh : BH
vuong
goc vdi IH.
Cau 6. Cho hinh binh hanh ABCD. Qua mot dii'm S trong hinh binh hanh
ABCD
ke
dudng
thing
song song
vdi AB Ian
lirpt
cat AD, BC tai M, P
va
cung
qua S ke dirdng thang
song song
vdi AD Mn
lirpt
cat AB, CD
tai
N, Q. ChiJng minh 3 dirdng thing AS, BQ, DP
ddng
quy. -
BAI
GIAI

2.
Ta c6 :
2x - y
1
ta
dugc
nghiem
(ji; y) = (2; 1).
Suy ra :
X
+ y 3
X
+ —
X
1
^
X
+ — + — + X
X
1^
X
+ —
X
4 1
X
+ —
X
( 1
+
X

X
+ -
x^^
V
v
X
+ - = 3 (vi X > 0)
X
3 1
( 1^
3
' 1^
X
+ —
- 3
X
+ —
I
x; ^ x;
= 18
4 1 ^
X
+ —
( 1 3
V
X
=
3.47-18
= 123.
Cau 3. Dieu kien : x > -

1
=
V3x
+ 10 ci>
VSx
+ 1=4 » X = 5.
Vay phifoing
trinh
c6 2
nghiem
la : x = 0; x = 5.
Cau
4.
a)
Ta CO : P = Sx" +
9y-
-
12xy
+ 24x - 48y + 82
= (X- - 8x + 16) +
(4x-
+
9y-
-
12xy
+ 32x - 48y + 64) + 2
= (X - 4}- + (2x - 3y + 8)' + 2 > 2.
fx
= 4
Dau "="

(2) => 3 - z'' +
3xy(3
- z) = 27 - 27z + 9z' - z'*
o 1 +
xy(3
- z) = 9 - 9z + 3z- o (3 -
z)(xy
+ 3z) = 8
Vay
cac
nghiem nguyen ciia phufang
trinh
la :
(1;
1; 1), (4; 4;
-5),
(4; -5; 4), (-5; 4; 4).
Cau
5.
(Hiiili
7)
a)
Ve
tiep tuyen
(d)
tai
B
ciia diidng tron
(O).
Ta CO

ciia dudng tron
(J).
Ta
CO B2 =
Ml
. Ma Ci =
Mi.
Suy
ra B2 =
Ci
=>
(d")
// AC
20
Ma
(d) 1
JB tai
B. Suy ra AC ±
JB.
Ma
AC 1 01 (01 la
ducrng thSng
noi
tam)
=> JB // OI
Mat
khac
OB 1
MN (chufng minh
cau a)).

doan
BI.
Vay
PK la
dudng trung binh ciia
tain
giac
BHI.
Suy
ra PK //
IH
=>
IH
1 HB
(dpcm).
Cau
6.
(Hinh
8)
Goi
I la
giao
diem ciia
DP
vdi
NQ.
Goi
K la
giao
diem ciia

PTTH CHUYEN LE HONG PHONG, TPHCM
De thi tuyen
sinh
vaa idp
10
(Ban
A,
B) nam hoc
2003
-
2004
Cau
1. Cho
phucfng
trinh
x^
-
2mx
- 6m - 9 = 0 (c6 an so la x).
a)
Tim
m de
phuong
trinh
c6
hai nghiem phan biet
deu am.
b)
Goi Xi, X2 la
hai nghiem ciia phaang

a)
x^y
+
xy^
= 30
b)
2
+
V2x
-
x^
+ 7
xy
= -64
i_l
- i
X y 4
Cau 4. ChiJng minh
rhng
neu a + b > 2 thi it nhat mot
trong
hai
phuang
trinh sau c6
nghiem
: + 2ax + b = 0; + 2bx + a = 0.
Cau 5. Cho diTcrng tron tarn O
du&ng
kinh AB. Goi K la trung
di§m

dinh.
Cau 6. Cho tam
giac
ABC c6 BC = a, CA = b, AB = c va c6 R la ban
kinh
dudng
tron
ngoai tiep thoa man h$ thiJc : R(b + c) =
aVbc
. Hay
dinh
dang tam
giac
ABC.
BAIGIAI
Cau 1.
a) Phircfng
trinh
c6 hai nghiem phan
biet
deu Sm khi va chi khi :
A' > 0
S <0
P > 0
m^
+ 6m + 9 > 0
2m
< 0 o
-6m
- 9 > 0

1
x^ + xy y^ + xy
> 4.
Dieu
ki$n
: -x" + 2x + 7 > 0 c=. 1 - 2V2 < x < 1 + 2^2
Taco:
-x'+ 2x + 7 =-(x - 1)'+ 8 < 8.
3
3(V2-1)
Do do : A =
2 + V2x - x^ + 7
3(V^-l)
V$y gia tri nho nhat cua bieu thufc A la , dat duofc khi x = 1.
Cau
a)
3.
Dat u = X + y, V = x.y. H| da cho c6 dang
Giai
h$ nay tim
diTOc
(u; v) = (6; 5), (5; 6).
x
+ y = 6 _^ |x + y = 5
u
+ V = 11
u.v = 30
Giai
he : va
xy =6

= -8
Cau
Cau
a)
b)
X
- y = 16
Vay nghiem (x; y) ciia he phirang
trinh
la (8; -8).
4. PhiTdng
trinh
x'^ + 2ax + b = 0 c6 biet so Aj = a^ - b .
Phirang
trinh
x^ + 2bx + a = 0 c6 biet so Ag = b^ - a .
Ta CO : Al + A2= (a^ - b) + (b'^ - a) = (a - 1)' + (b - if + (a + b - 2) > 0.
Do do trong hai so A;, A^ C6 it nhat mot so khong am nghia la c6 it
nha't
mot trong hai phirgmg
trinh
da cho c6 nghiem.
5. (Hinh 9)
Ta CO : AAKM =
ABNK
(c.g.c).
Suy ra AMK = BNK .
Tir
ket qua cau a)
AAMK

ra
MK
la
ducfng phan
giac
ciia DMN.
d)
Gia
siif
du'cfng thSng vuong
goc
vd'i
BM
tai
N cat
ducfng
thflng
AK
tai
E.
Nhan
thay
rang til
giac
BEKN
npi
tiep,
suy ra
AEB
=

do
dai
dudng
kinh
va
day
cung
ta
c6 :
2R
>
BC
= a va b +
c>2Vbc,
suy ra
R(b + c) >
aVbc
.
Dang thiJc
xay
ra
khi
va
chi
khi tam
giac
ABC
vuong
can
tai

-
2004
Cau
1.
a)
Thu
gon
bieu thiJc
A =
nghiem thi phuong
trinh
sau
luon
c6
nghiem
;
^yttk
(an
~
mb)x-
+
2(ap
-
mc)x
+
bp
-
nc =
0.
^^^u

d
diem
E (D va E
khac diem
A).
a)
ChiJng
minh
; D,
H,
E
thang hang.
b) ChiJng
minh
:
MAE
=
ADE
va
MA
vuong
goc
vdi
DE.
c) ChiJng
minh
bon
diem
B, C, D, E
cCing thuoc

c6
hai
dudng
cheo
AC
va
BD
ciing bang canh
day Idn AB.
Goi
M la
trung
diem ciia
CD. Cho
biet MBC
=
CAB
.
Tinh
cac
goc
ciia
hinh
thang ABCD.
3V2-2V3
V2-V3
\3V2
+
2V3
b) Tim

- 4 = 0.
Cau
3.
Phan
tich
thanh
nhan tuT
: A =
x"*
-
5x-'
+
lOx
+ 4.
4
.
Ap dung
:
Giai
phiTcfng
trinh
:
x2-2
=
5x.
Cau
4.
Cho
hai phuang
trinh

+ 2V3
V2-V3
^
76(73
+ 72
^
i75-75U
73 + 72 72 -73 \
1
p^7i)(73->^)
72-73
-(73-72
=
-1 (vi 73 - 72 > 0 )
Vay
A =
-1.
b) Dieu
kien
: x > 2.
3-2
73
=
7x
- 1 - 27x'^ +
7x + 7
- 67x - 2
=
7x
- 2 - 27x - 2

l<x-2<9
<=>
3<x<ll
Vay gia tri nho nhat ciia yla2 c? 3<x<ll.
Cau2.
[x
+ y + xy = 2 + 3V2 (1)
(2)
a)
y^
+ = 6
Ta CO
<=>
X + y = 2 + V2 (3)
X + y = -4 - V2 (4)
y^
+ x^ + 2(x + y + xy) = 6 + 2(2 + 3A/2)
(X- + 2xy + y^) + 2(x + y) = 6 + 4 +
(X
+ y)^ + 2{x + y) + 1 = 3- +
2.3V2
+ (72)^
(x + y + = (3 + V2)^
^x + y + l = 3 + >^
x + y + l =
-3->/2
Tir(l)
va (3)
CO
xy = 2V2

x^ = 4 - x'^
X > 0
2x^ = 4
X
= V2 (thoa dk -2 < x < 2)
Vay nghiem cua phuomg
trinh
da cho la x = -\/2 .
Cau 3. A = x' - 5x' + lOx + 4
= x"* - X'* - 2x^ - 4x-' + 4x' + 8x - 2x' + 2x + 4
= X- (x^ - X - 2) - 4x(x^ - X - 2) - 2(x' - x - 2)
= (x- - X - 2)(x^ - 4x - 2) = (x' - 2x + x - 2)(x- - 4x - 2)
= [x(x - 2) + (x -
2)|(x^
- 4x - 2)
Vay A = (X - 2)(x + IKx" - 4x - 2).
Ap
dung : Dieu ki#n - 2 ^ 0 c=>
x^±^/2
+4
x^ -2
= 5x
x" + 4 = 5x(x^ - 2)
x" - 5x' + lOx + 4 = 0 (X - 2)(x + IXx^ - 4x - 2) = 0
x-2 = 0
X + 1 = 0
x^ -4x-2 = 0
X = 2
X = -1 <=>
x^ - 4x + 4 = 6

aC + bB = 0 <^
a
27
(4)
tro
thanh
: 2Bx + C = 0 ci>
2Bx
+ -B = 0
a
-
B = 0 ta
CO
X
ttiy
y
-
B 7^ 0 ta
CO
X =
2a
(3)
CO
nghiem.
(3)
CO
nghiem.
2. Neu
A ^ 0. Ta
CO

4acAC
b"B"
=
(cA
+ aO' >
4acAC
>
b'AC
b^
> 0
B^
-
AC
> 0
Vay
A'
> 0 => (3) c6
nghiem.
Trircfng
hop
phirong
trinh
(2) v6
nghiem, chiing minh tirong tiT nhiT tren
duoc
(3)
CO
nghiem.
Tom
lai

tai
A c6
AM
la
trung tuyen
(gia
thiet)
AM
=
MB
=
MC
= — .
AMAC
can tai
M ^
MAE
=
MCA
(1)
HA
=
HD (vi
A,
D e
(H; HA))
AHAD
can tai
H =>
ADE

=
DAE
.
Do
do
ADE
+
DAI
=
90°
^
Hinh
10
AID
=
90°
MA
1
DE.
c)
Tir
(2) va (3)
ta c6 :
ADE
=
MCA
=>
B,
C,
D,

thiet), OM
1
BC
=>
AH
//
OM.
va MA
1 DE
(cau
b),
OH
1 DE
MA
//
OH.
TiJ giac
AMOH
c6
AH
//
OM
va
MA
//
OH
nen tuf giac
AMOH
la
hinh

HAE
= 60°
AHAE
deu
AE
=
HE
= a,
HK
=
AHVS
aV3
Do
do
Vay:
EC
=
AC
- AE = 2a - a = a.
1
aVs
V3 .
S,i, c
= -
EC.HK
= -
•
a
•
= —

ABC
-
MBC
Goi
N la
trung diem
canh
AD
=D
MN
la
dudng trung binh AADC
=>
MN
//
CA
=> DXC
=
DNM
(2)
CAB
=
MBC (gia
thiet)
Hinh
11
Tir
(1) va (2)
c6
ABM

=
90°.
=> AB
la
ducyng
kinh
ciia ducmg tron ngoai tiep AMAB
=> AMB
=
90°
. Ma
MA
=
MB
(tinh
chat
doi xufng true).
Do
do
AAMB
vuong
can tai M s>
Ta
CO
:
AABC
can tai A
(AB
=
AC).

nam hoc
2002
-
2003
Cau
1, Tim gia tri cua m de phifang
trinh
sau c6 nghi^m va
tinh
cac
nghiem ay theo m :
X + I - 2x + m
I
= 0.
Cau
2. Phan
tich
thanh nhan
tilf
: A = x'" + x'' + 1.
Cau
3. Giai cac phucfng
trinii
va he phirong
trinh
:
b)
Vx + 2 +
3V2x
- 5 + = 2A/2

MK MI
Cau
6. Cho tam
giac
ABC. Gia
sijf
cac
dacrng
phan
giac
trong
va phan gi^c
ngo^i cua goc A cua tam
giac
ABC Ian
liTot
dt
duemg
th^ng BC tai D,
E
va CO AD = AE.
ChiJng
minh
: AB" + AC^ = 4R- vdi R la ban
kinh
diTcJng
tron
ngoai
tiep
tam

+
Xet m < 0 : phUdng
trinh
da cho c6 bon nghiem, hai nghiem duang. hai
nghiem am (do P < 0) thoa dieu kien x < 0.
1
- Vl - 4m 3- V9-4m
Hai
nghiem am la : x = ^ ; x = ^ .
Vay m < 0 thi phifong
trinh
c6 nghiem :
X = 0; X =
1
- Vl - 4m
X =
3 - V9 - 4m
2 • 2
Cau
2. A x'" + x' + 1
=
x'° + x% x« - x" - x« - x^ + x^ + x« + X'' - x« - X'' - x^ + x^' +
+
x'* + x'* - X-' - x'-^ - X + X^ + X + 1
=
x'\x- + X + 1) - x^(x' + X + 1) + x'^(x' + X + 1) - x^x- + X + 1) +
+
x''(x- + X + 1) - x(x- + X + 1) + l(x- + X + 1)
Vay A =
(X-+

= 9 + 12 = 21 => VA^ = V2T.
X|
= 3 + V2I ; xv = 3 - V2T .
4 X 4 4 •>
* Vdi V = - , ta CO : = - <=> x" - 12 = 4x <=> x" - 4x - 12 = 0
3 3x3
A'
= 4 + 12 = 16
VA^ = 4 .
x,( = 2 + 4 = 6; X4 = 2 - 4 = -2.
PhUong
trinh
c6 bon nghiem la :
X, = 3 + A/2T ; Xv = 3 - V2T ;
x.) = 6;
X4
= -2.
b) Dieu
kien
x > - . Ta c6 :
Vx
+ 2 + 3/2x - 5 +
-y/x
- 2 - V2x - 5 = 2V2
2
o
o
o
o
<=>

c)
xy^
- 2y + Sx^ =0 (1)
y-
+ x-y + 2x = 0 (2)
* Xet X = 0 thi y = 0, he c6 mot nghiem
X = 0
[y = 0
* Xet X
7i
0,
nhan
hai ve ciia (2) vdi x roi
trCr
cho (1) ve theo ve ta c6 :
x'V +
2y - X" = 0 y(x'* + 2) = x'
y
=
(vi
x'* + 2*0).
Thay vao (1) ta c6 : x
(
2 N
U
+2
-2
^ x^
x^
+2j

la :
X = 0
y
= 0
X = -1
y
= 1
X =
-2
Vs
-6
Cau 4. Ta CO : x^ - 5x + 7 =
5
X —
2
+ — > 0. Do do y xac
dinh
vdi moi x.
4
y
= ^
x^
- 5x + 7
c:> yx" - 5xy + 7y = x' c:> (y - l)x' - 5xy + 7y = 0
* Xet y = 1, ta CO : -5x + 7 = 0 o x = -
5
* Xet y ^ 1, ta c6 : A = 25y' - 28y(y - 1) = 25y' - 28y- + 28y
= -3y- + 28y = y(-3y + 28)
De CO x thi A > 0 co
y

canh AB, DC cua tam
giac
MBA, MDC.
AB DC
Ta CO :
MI
MH
(1)
Mat khac : BMD = BMA + AMD ,
AMC = DMC + AMD va BMA = DMC ^ BMD = AI
Xet AMBD va
AMAC
c6 : BMD = AMC ; MBD = MAC (hai goc noi
tiep Cling chan cung MC).
Do do : AMBD co
AMAC.
MH,
MK Ian luot la dudng cao ufng vdi canh BD, AC ciia tam
giac
RD AC
MBD, MAC. Ta CO : — = (2)
TO (1) va (2) ta c6 :
Vay :
BC AC
MH
AC
MK
AB
MK
AB BD + DC BC

AD, AE la hai tia phan
giac
ciia hai gdc ke bii BAG va CAx nen
DAE = 90° .
ADAE
vuong
CO AD = AE (gia thiet) nen la tam
giac
vuong
can
=^ ADE = 45°.
sdADE =
'^^^^'^^^
^
SdAC
+
SdBF'=
90" (3)
2
Tii
(1), (2) va (3), ta CO : GB = AC GB = AC.
ABAG
vuong
tai B nen : AB' + BG' = AG' => AB" + AC' =
(2R)'"
=> AB' + AC' = 4R' (dpcm).
DE
9
TRUCfNG
PTTH

+ - + - (a > 0, b > 0, c > 0)
a^b^c a b c
c) a' + b' + c' + d' + e' > a(b + c +. d + e) vdi moi a, b, c, d, e.
Cau 3. Giai cac phuong
trinh
:
«\ 2x „ , ^ 4x 5x
a) x'+ = 8 b) — + — = -1
X - 1 x^ - 8x + 7 x^ - lOx + 7
Cau 4. Cho tam
giac
ABC cd ba gdc nhon noi tiep trong difdng tron tam 0
va true tam la H. Lay diem M thuoc eung nho BC.
a) Xae dinh vi tri ciia diem M sao cho tuf
giac
BHCM
la mot
hinh
binh
hanh.
b) Vdi M lay bat ki thuoc cung nho BC, goi N, E Ian lugt la cac diem doi
xiing
cua M qua AB va AC. Chilng minh ba diem N, H, E thSng hang.
Xac dinh vi tri cua M thuoc cung nho BC de cho NE cd do dai Idn
nhat.
35
Cau
5. Cho
dLfdng tron
co

l)x^
-
2(m
+ 2)x + m - 3 = 0
* Vdi
m+l =
Oc:>m
=
-l
PhUcfng
trinh
trd thanh
: -2x - 4 = 0 <=> x = -2
Vay khi
m =
-1, phucfng
trinh
c6
nghiem
x = -2.
* V6i
m + 1
7^
0 ci. m
;t
-1
A'
=
(m
+ 2f -

— •
6
Vay phUdng
trinh
c6
nghiem
<=> m > —.
6
CaU
2.
a)
^
2a- + 2b' + 2c- - 2ab - 2bc - 2ca > 0
^
(a- + b- - 2ab) + (b" + c" - 2bc) + c" + a" - 2ca) > 0
^
(a - b)- + (b - c)- + (c - a)- > 0
(dung)
Do
do a" + b" + c' > ab + be + ca la bat
ding thufc dung,
b) Ap dung
cau a) ta c6 :
a»
+ b« + c« > a^b^ + b^c^ + c^a^ =
(aV)"'
+
(bV)"
+
(cV)'''

d"
+ e' > a(b + c + d + e)
a"
+ b" + c~ + d' + e' - a(b + c + d + e)>0
a"
+ b" + c' + d' + e" - ab - ac ad - ae) > 0
a"
+ b" + c" 111
"
a ^ b ^ c
•
+ b^
- ab
+
c" - ac
—
+
d^
- ad
4
a
2
—
+ 8 - ae
4
>
0
b) Dieu kien
: m > — ; m
5^ -1.

X2)
- 17 = 0 «
16(m-3)^8(m.2)_^^^^
m
+ 1
m
+ 1
16(m
- 3) +
8(m
+ 2) -
17(m
+ 1) = 0
16m
- 48 + 8m + 16 -
17m
- 17 = 0
7
7m
-49 = 0 o m = 7
(thoa dieu kien
m
;t
-l;
m > — )
6
Vay
m = 7
thi phucfng
trinh

thuTc
dung)
Do
do
a" +
b"
+ c" +
d-
+ e'- >
a(b
+ e + d + e) la
bat
dang
thufc
dung.
Cau
3.
a) Dieu kien x-\*Qoxi^\.
2x
Ta
CO
:
X'
+
o
X' - X- + 2x = 8x - 8
X
- 1
X''
- X- - 6x + 8 = 0

= 0
if
X
+
—
2)
-11 = 0
4
37
X
= 2
1
Vl7
X
+ - = ±-—
2
2
<=>
X
= 2
±Vl7
- 1
(thoa dieu kien
x * 1)
X
=
Vay
phucfng
trinh
c6 ba

-
•I
x-l,.l
X
X
=
-1
Dat
t =
X
- 10 + - .
Phircfng
trinh
trd thanh
:
X
c:>
4t + 5t + 10 =
-t'-
- 2t
t
+ 2 t
o
t-+
lit+10
= 0 c:> t =-1
hoac
t =-10
(vi
a - b + c = 0)

+ - = 0
cx>
X- + 7 = 0
Vay phirang
trinh
c6 hai
nghiem
la
Cau
4.
(Hinh
14)
a)
Ta
CO
:
AH
1
BC, CH
1
AB.
Tur
giac
BHCM
la
hinh binh hanh
c:.
BH
//
MC

X e 0
9
+
V53
9 - >/53
Hin/i
14
AMB
=
ACB (hai
goc
noi tiep ciing
chan
mot cung AB)
38
Cau
Suy
ra
ANE
= ACB
.
Ma
AHB
+
A'NB
=
180°
==. tir
giac
NAHB

=>
N, H,
E
thSng
hang,
NAE
= 2BM: ,
Ve
AK 1 NE, K e NE.
Ta
CO
:
AM
=
AN,
AM
=
AE (tinh
chat
doi xufng true).
=> AN
= AE
AANE
can tai A, ma
AK
la
duo'ng
cao
iz>
AK vCra

BAC
khong doi.
NE
16-n nhat
CD
AM idn nhat
co
AM
la
dudng
kinh
cua (O) <=> M la
diem doi xiing ciia
A
qua
O.
Vay khi
M la
diem doi xufng ciia
A
qua
O
thi
NE
16'n nhat.
5.
(Hinh
15)
Ta
CO

ta c6 :
AM
+AN
> VAM.AN
Do do
s,vM^:
>
VAM.AN
>
VMI.AN
Hinh
15
SAMN
= -
MI.AN
Ml. AN
= 2SM
AiMN
39
Ta CO
: S
AMN
AMN
SAMN
^ 2S
AMN
Dau "=" xay
ra o I = A <:=.
MN
1

so' nguyen
x
thoa
: x"*
+
8 =
VVSx
+ 1 .
Cau
2.
Cho
n la so
nguyen duong. Chufng minh
ta
luon
c6 bat
dang thufc
12
3 n 3
-
+
—
+
—
+ +
— <—.
3"
4
3
3^

Cau
5. Cho tam
giac
ABC
c6 ba goc
nhon.
D la
mot diem tren doan
BC.
Dat
BC = a,
CA
= b,
AB
c,
AD
=
d,
DB =
m, DC
= n.
1.
ChiJng
niinh
: d"a =
b"m
+ c'n -
amn.
2. Cho biet AD
la

+ 1)
(x"
+
8)'
= 7V8x + 1
» x'
+
16x'
- 392x + 15 = 0
c=.
x" -
3x'
+
Sx'
- gx" +
gx'
-
27x'
+
43x'
-
129x'
+
129x'
- 387x
-
5x + 15
«
' x'Hx -
3)

Qx^
+
43x2
^
i29x
-5 = 0
X
= 3
x^ + 3x'* + 9x3 +
43x2
+ 129x - 5 = 0
Ta thay
x = 0
khong
la
nghiem ciia
(*)
vi
: -5 0.
x?^0tac6x>0vax€
Z nen x > 1.
Do do
:
x"'
+ 3x'' + 9x' +
43x^
+ 129x > 5
=>
(*) v6
nghiem nguyen

chi
c6
mot nghiem nguyen
la x = 3.
m
+
0,5 m
+
1,5
Cau
2.
V6i
m
nguyen duong,
ta c6 :
m
2.3
m-l
2.3"
Thay
m
Ian lUOt bdi
1; 2; m. Ta c6
1 1,5 2,5
3^2 2.3
2
2,5 3,5
32
2.3
2.32

- 2 > 0
4
- X > 0
X
> 0
2
< X < 4.
Cau
3. Dieu kien
Ap
dung
bat
dang thufc Cosi
cho
hai
so
khong am,
ta c6 :
1
• ; ,
/x
- 2
+
4 - X
V(x-2)(4-x)
=
VV(x
- 2){4 -
X)
< J ^ = 1

^4
^
x
+
GxVs^
<
x^
+
30
Vay
2 < X < 4 la gia
tri
cin
tim.
Cau
4.
* CdcVi
7 ;
Taco:
(2a + 3)(a - 3)" > 0 <=• (2a +
3)(a^
- 6a + 9) > 0
<=:>
2a' - 12a- + 18a + 3a- - 18a + 27 > 0
CD
2a'' - 9a- + 27 > 0
Dau
"=" xay ra c=> a = 3
TLfOiig
tu, ta CO : 2b'' - 9b' + 27 > 0, 2c' - 9c' + 27 > 0.

2
3
Do
do : a' + -
(a''
+ 9) > 6a' c=> 2a'' - 9a' + 27 > 0
Tuong
tu
nhu'
each
1,
giai tiep.
* Cdc/i
3 : Bai
toan
phu :
ChiJng minh rang
i
a,b, + avb, + a,b.,
|
< ^(af + a|
+a5)(bf
+ b^ + hj)
(Bat dang thiJc
B.C.S)
Dau,"="xayra
« ^ ^ ^1 ^ ^
bi
b, bg
Dodo:

c''> 81
Dau
"=" xay ra <=> a = b = c = 3.
Vay
gia
tri
nho
nha't ciia
a' + b' + c' la 81.
Cau
5.
(Hinh
16, 17)
1.
Ve AH 1 BC, H e BC
*
Xet D n^m
tren duo-ng thang
HC.
AHAB
CO H = 90° ,
theo
dinh
li
Pitago
ta c6 :
AH'
+
BH'
=

d' = c' +
BD(DH
- BH)
=> d'n = c'n +
mn(DH
- BH)
ChiJng minh tuong
tu ta c6 :
d'm
= b'm +
mn(-DH
- CH)
Ta
CO : d'm + d'n = b'm + c'n +
mn(-DH
- CH + DH - BH)
d'(m
+ n) = b'm + c'n +
nm(-CH
- BH)
d'a
= b'm + c'n - amn
*
Xet D nam
tren duo'ng thang
HB.
Chufng minh tUo'ng tif tren
ta
cung
c6 : d'a = b'm + c'n - amn.

AB.AC.
AE
AD
AD'
=
AB.AE
43
DE
11
TRl/dNG PTTH CHUYEN LE
H6NG
PHONG,
TPHCM
De thi tuyen sinh vdo Idp 10 (Ban A, B) nam hoc 2000 - 2001
Cau
1. Cho phuong
trinh
: x' - 2(m + l)x + m" - 4m + 5 = 0 (c6 an so la x).
a) Dinh m de phiidng
trinh
c6 nghiem.
*
b) Dinh m de phuong
trinh
c6 hai nghiem phan biet deu difOng.
Cau
2. Giai cac phuong
trinh
va he phiTcfng
trinh

b) Goi E la
trung
dii'm ciia doan BC. Dudng thSng OE cAt diTong
tron
(0)
tai
diem K (khac diem N). Chufng minh
tiif
giac
ADEK
la mot
hinh
binh
hanh.
c) Chufng minh rang khi C di chuyen tren dudng
tron
(O) thi MN luon
luon
tiep xiic voi mot duang
tron
co
dinh.
Cau
5. Cho hai tam
giac
ABC va DEF c6 cac goc deu nhon va c6
ABC = DEF, BXC = EDF , AB = 3DE.
Chufng minh rang ban
kinh
dudng

a ^ 0 1*0
j^-
> 0 6m - 4 > 0
S > 0 ^ l2(m + 1) > 0
P > 0 m'^ - 4m + 5 > 0
6m
> 4
c=>
<!
m + 1 > 0
(m-2)^ +1 >0
2
m
> —.
3
Cau
2.
a) x'' + 3x'- + 3x + 1 = 0 (x + l)' = 0
Vay phirong
trinh
c6 nghiem la -1.
x
= -1
b)
x
- y = 3
X
= 3 + y
27
+'27y

c a \ a
b) ?^ + — >2h
(theo
cau a)
c a
ab ca
Chufng minh tifong tu cau a) ta co : —- + — > /a ;
^ , ab be ab ca be ca , „ „
Do do: — + — + — + — + — + —>2b + 2a + ^c
c a c b a b
ab be ca ^ , „
<;:> — + — + — >a + b + c.
cab
c) Vdri a, b > 0. Ta c6 :
(a + b)(a - b)'> 0 (a +
b)[(a'-
ab + b") - ab| > 0
<=> a'' + b'' - ab(a + b) > 0 c:> a'' + b' > ab(a + b)
*
a + b
a^_+b^
2ab
Tiro-ng tir ta c6 : """" > -^-^
2bc 2
+ ^ c + a
2ca " 2
n
i'
a3+b
Do do : +

CDNE c6 CBN = DNE = DCE = 90° nen la hinh chuf nhat.
Goi I la
giao
diem cua DE va CN.
Taco:
IE = IN => AlEN can tai I lEN = INE.
Hinh
thang ACNK (AC // ON) noi tiep dudng tron (0) nen la hinh
thang can =- INE = AKN .
Taco:
AKN = lEN (=
INE)
^ AK = DE.
> tiJ
giac
ADEK la hinh binh hanh.
, AK // DE, AC // ON
1
-
1
c) sdMN = sdMC + sdCN = - sdAC + -
sdBC
= 90°
1
2 2 j
MN
la
canh
ciia hinh vuong noi tiep (0; R) '
RV^ ' _ ' _J

= IE (= r)
Do do AOAB ^ AIDE
Hinh
20
Hinh
19
AOAB can tai O.
AIDE
can
tai
I.
OA _ AB R ^ 3DE
ID"
" DE ^ r ^ DE
R
= 3r.i
DE
12
TRUONG
PTTH
CHUYEN
LE
HONG
PHONG,
TPHCM
De thi
tuyen
sinh
vao Idp 10 chuyen
Toan

chinh no va 1, nhUng chi c6 3 Ud'c so nguyen to
khac
nhau. Gia
siJf
tong
ciia cac Uo'c so nguyen to' la 20,
tinh
gia tri nho nhat c6 the c6 ciia N.
Cau 4. Tim tat ca cac so' nguyen x, y, z thoa phuong
trinh
:
3x- + 6y' + 2z' + 3y-z- - 18x - 6 = 0.
Cau 5. Dien tich tam
giac
ABC la 1. Goi A,, B,, C, Ian luot la trung diem
BC,
CA, AB. Tren cac doan
AB,,
CA,,
BC, Ian lugt chon cac digm K, L,
M.
Tim gia tri nho nhat ciia dien tich phan chung cua hai
.AKLM
va
AA,B,C,.
47
BAI
GIAI
Cau 1. Bai
toan

A
+ a
A+a+B+b+c+d A+a+c+d
B+b+C+c
C
+ c
Ma
A
+ a
C
+ c
B+b+C+c+a+d C+c+a+d
A
+ a C + c
A+a+c+d
C+c+a+d C+c+A+a+b+d C+c+A+a+b+d
Do
do :
A+a+B+b ^ B+b+C+c C+c+A+a
A+a+B+b+c+d B+b+C+c+a+d C+c+A+a+b+d'
Cau
2.
a, b > 0
theo
bat
dfing
thiJc
Gosi
cho hai so
du'Ong

x^
+ y^ + 2xy
>
4 + 2 + 5=11
-
+ 2
j4xy.
+
2 +
4xy
4 (x + yf (x + yf (x + y>
A
> 11. Dau "=" xay ra x = y = -
2
Vay
A dat gia tri nho
nhat
la 11.
Cau
3.
Goi cac
irdc nguyen
to cua so N la p, q, r va p < q < r.
q
= 5; r = 13
q
= 7; r = 11
=>p = 2; q + r=18=^
Vdi
a, b, c e N va (a + l)(b + l)(c + 1) = 12.

=> y" < 2- => y"* = 0^ 1'; 2". Ta Ian
lifcJt
xet :
y-
= 0 ==> (x - 3)' = 11. V6 li !
y-
= 1- ^
(X
- 3)- = 3- => X - 3 = ±3 => X 6 hoac x = 0
Co
cac
nghiem
(x = 6; y = 1; z = 0); (x = 6; y =
-1;
z = 0);
(X
= 0; y = 1; z = 0); (x = 0; y =
-1;
z = 0).
y'
= 2' =>
(x-3)'
= 3.
Voli!
'et
z- > 9. Ta c6 3x- + 6y- + 2z- + 3y-z- - ISx - 6 = 0
C5
3(x - 3)- + 6y' + 2z' + 3y^z' = 33
thi
2z^ + 3y-z^ > 2.9 + 3.1.9 > 33

= 9
z'
> 9
All
BM ^
——
< < = 1
IH
MA CjA
A,l
< IH
•hijfng
minh
tuong
t\i ta cd :
'HB,E
<S
HEG
'
^GC,N
<s,
GNF
•
Do do : SFA,I +
SHB,E
+ SGC,N ^ ^vm + S
HEl
;
+S,
'GNF