Duong ChtmgminhrangCDf ME' F AB < AC' cdrcduongcaoBD virCE'Gqi ABC gi6c tam Cho 2.0 didm... PHONGGD&DTHUYENAN DUONG DAP AN DE THI CHQN HQC SINH GIOI.[r]
Trang 1PHONG GD&DT HIYEN-AN DUONG
oE csiNH THuc
Bhi 1: (2.0 ttidm)
1 1 1
t I t - n
a C h O - + - t - - v '
x y z
KV rHI cHoN HQC sINH GIoI t'6P a
Nam hoc 2011 '20L2
MON: TOAN
a + b + c
+ F D F E : A F 2 '
m d n a < b S c '
Tinh gi6 tri cua bi6u thuc
1 1 = = = - x - + / ' Y Z Y 2 + Z z x z ' + Z x Y
r l l
b C h o a , b , c * 0 v A a + b + c r 0 t h o a m d n d i d u k i Q n
- * U * ; =
I * I * r
U z o t l
'
b 2 0 l l C 2 0 l I
C h t m g m i n h a n B m
(x-2)' ,(!:] l'-,, (+l =o
to[-.t,1
l + x + x 2 + * ' : Y '
AB = 5cm'
AB o E'
a
-Hdt -G i d m t h i s o l : ' r " " r " ' r " i " ' r " " '
Trang 2PHONG GD&DT HUYEN AN DUONG DAP AN DE THI CHQN HQC SINH GIOI
a Tir gi6 thi6t ta c6: xy * xz + yz: 0
V 6 v A _ x ' ( z - y ) + y ' ( x - z ) + z ' ( y
- x )
' YJ "
b Ta c6:
a b c a + b + c a b c a + b + c a b c ( a + b + c )
olu+c=o<+lb=-c
l t
Khi d6 ta c6:
1 l
ffi=ry=
1 1 1 1 1 1
J - - J = I I
-a 2 0 1 3 b 2 0 1 3 ' c 2 0 1 3 -a 2 0 t 3 ' ( _ -a ) t 0 , , C 2 0 1 3
0.25d
a20t3
I
= -a20t3
Suy ra
a 2 0 1 3 + 9 2 0 1 3 * a 2 0 1 3
1 1 1
_ I l
-a 2 0 1 3 6 2 0 1 3 C 2 0 1 3
l0u:v.
0.5d
0.75al 0.75d 0.5d
0.25d 0.25d
Bii 2: (2.0 didm)
DiK: x * +l
v - 1 , r ' )
D [ t u - ' x - L , u = ^ " ( l )
* N 6 u u : v
" 6 * - 2
- x + 2 g1=
x + 1 x - l
* N6u l o u : v c 6 I o * - z = * * 2 o
Biri 3: (1.0 ili6m)
T a c 6 : * ' +
" * l : ( x * l ) t * 1 t o v d i m q i x'
1 0 ' 2 0
Ou-v;:g <+ u:v hoflc
0 ( x - : ) ( e x - 6 ) = s
[ x = 3
*"1 2
l X =
-L 3
Trang 3NOn (1 * x * x2
( 5 x 2 + 1 1 x + 7 )
€ * ' < i + x * x
do d6 tr: 1x+1)3
+ r ' ) - ( l + x + x t ) I * x * x t + x ' < ( 1 + x + x 2 +
t + *' < (x+2)2 hay x3 y' (x + 2)3
x3) +
0.25d
0.25d
S u y r a ( x + 1 ) 3 : 1 + x + x2 + x3 e[* = o,
l x - - l
N 6 u x : 0 t h i y : 1
N 6 u x : - 1 th i y : 0
Bhi 4: (2.0 tliim)
Ggi K li giao di€m cua AM vd EC, tr€n do4n MK l6y di6m
I s a o c h o M I : M A : 6 c m
Tri gi6c ABIC ld hinh binh hinh
=)AB = IC = 5cm,AI = 2AM =l}cm,AC = l3cm
= fr =900
L4i co Bm = diM = 900 B
ABEK co BC, KM la c6c dulng cao
Me MB : MC vi DMC = BMK :+ ADMC = AKMB(c.g.c)
Tt (I) vd (II) suy ra EMI DC
Bhi 5: (2.0 tli6m)
Tr€n do4n thing AF laY di€m M sao cho
0.5d 0.5d
FME=Fil AADB.,,AAEC-> D -49
AE AC
AADE ,oAABC :t ^ffiE =.ffib
Do do FME = ABC = AME = ABF
AAME , AABF
A M A E ^ F ^ I
FD AF
zb>b+ a > c =+ 4b - c > 0 = (b -c).(ab - c) < 0
M d : ( a + b + c ) 2 < ( 2 b + c ) z
(l) (2).
l.0iI
0,5d
0,5d