Question

用因式分解法解下列各题

4（x-3）²=25（x-2）²

Answer 1

4(X-3)^2 - 25(X-2)^2 移项
= [ 2(X-3)+5(X-2)] [ 2(X-3) - 5(X-2)] 平方差公式
= (7X-16)(-3X+4)
=0

X1= 16/7 , X2= 4/3

Answer 2

4（x-3）²=25（x-2）²
4x²-24x+36=25x²-100x+100
21x²-76x+64=0
(7x-16)(3x-4)=0
7x-16=0,3x-4=0
x=16/7,x=4/3

Answer 3

4(x-3)²=25(x-2)²
2(x-3)=±5(x-2)
2x-6=5x-10或 2x-3=10-5x
3x=4或7x=13
x1=4/3 x2=13/7

Answer 4

[5(X-2)]^2-[2(X-3)]^2=0
[5(X-2)+2(X-3)][5(X-2)-2(X-3)]=0
(7X-16)(3X-4)=0
X=16/7,X=4/3

Answer 5

两边开平方，得x=4/3