Tinh dQd i canh Be va dien tich tam giac ABC.. Chung minh r~ g: Dang thirc xay ra khi nao?
Trang 1Truong THPT Nguyen Hue
·Ta toan
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Kh3i IOAB Thai gian: 60 phut
Bi I: (3 di~m)
I Giai phuong trinh: ~2 X 2 - 3x +1=x-I
2/G o" lal va• bielen uan1 A : x+m = 111
I/G " o A h • h x -+ y +3x y= 11
r a i y p irongtrtn :
x+y-xy=1
~ 2 Tim m d~ h~ phuong trinh sau co vo s6 nghiern:
{mx+ y = m+1 x+m y =2 Bili 3: (2 di~m)
Trong m?~ phang toa dQqx y ~ho cac di~m A( 3;I , B(2;4)o 1/ Tim diem C tren true Ox de tam gia ABC vuong tai C
21 Khi C( I;0) hay tinh dien tich 0.ABCva ban kinh duo g trim ngoai ti~~ 0.ABC
Bili 4: (1 di~m)
Cho tam giacABC co AB = fi , AC = 2 ,A =45" Tinh dQd i canh Be va dien tich tam giac ABC
Bi 5: (Idi~m)
Cho a, b,c lacac s6 dirong Chung minh r~ g:
Dang thirc xay ra khi nao?
H~t
Trang 2nAp AN MON ToAN KHOI lOAB
~
csu :
Bai 1
{X -I> 0
2 x - - 3x +I= x - I
{X ~ I
x> 1
¢:::>{ 2- ¢:::>[ X =0 ¢::>X = I
x -x= O
x= I (co th~ trinh bay e ch khac)
Diem
2 x+m =m ( I )
x-I
-I m
Khi m = I: (2) ¢:::>O.x = -2 v n hiern ~ () vo n hiern
K~et u1a' : m - I: ±I Pt co'hn" rem x =- 2m
(kho g co tru ' o ' ng h p m =-1 thl ch 1 di~m)
0,5d
Id
Bai 2:
V l P = 2 => xy = 2 ¢:::> ¢:::>x = I;y = 2
" {S = -4 {x + y = -4 [ x = +I,y =-S
-V ~y h co4 n hiern:
0,25d
0,5d
0,5d
O,Sd
Id
{mx+ y = m+ I
2 x+ m y = 2
D= m ' -I D = m 2 +m - 2'
0,5d
0,5d
i
Bai 3:
(2 )
D = m -{m 2 -I = 0
,
0,2Sd
0,5d
0,25d
a/A(3;1), B(2;4)
A C =(a +3;-1); B e =( a - 2;-4)
a=-2
b l TLfca u a ta thay !'lASC v u n t~i C
0,5d
Trang 3D·le•l1tlc:i , h S=-I AC BC. =-17
B'a 'k'Inhat ngoai u .e~: R = -AB ~ J34
(chi tinh durrc AB, AC thl cho O,2 d)
0,5a
Bai 4:
10
ApdungDICOS I n: BC = AB - +A C - - 2AB A C cos A =2+4-2.,,2.2'2=2
D'"I~ t.c 11 tam glac : S= -) AB .AC·.sII1A=-") r; L :? 2 -12 = 1
0,50
0,50
Bili 5:
10 ~ b +~+~+3~ e ac a ab + l + b +l+e +1 a b e
~-+-+-~-+-
Ap dung b 1to~ng thirc Cosi:
b e +( 1 e ~ 2fb - : ' - ;;; ; = 2 ; :; a e +ab ~ 2 - -;;; ab +b e ~ 2' b
Cong v theo v~ ~ Dpcrn
Dan thirc xa ra ~ a= b=c
0,750
0.250
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