Question

用因式分解法解下列方程;

Answer 1

(4x-1)(5x+7)=0
4x-1=0 5x+7=0
∴
x1=1/4
x2=-7/5

x(x+2)=3x+6
x(x+2)-3(x+2)=0
(x+2)(x-3)=0
x+2=0 x-3=0
∴
x₁=-2
x₂=3

(2x+3)²=4（2x+3)
(2x+3)²-4(2x+3)=0
(2x+3)(x-4)=0
2x+3=0 x-4=0
∴
x₁=-3/2
x₂=4

2(x-3)²=x²-9
2(x-3)²-(x-3)(x+3)=0
(x-3)(2x-6-x-3)=0
x-3=0 x-9=0
∴
x₁=3
x₂=9

Answer 2

(1)解：4x-1=0或5x+7=0
∴x=1/4或x=-7/5
(2)解：x(x+2)-3(x+2)=0
(x+2)(x-3)=0
x+2=0或x-3=0
∴x=-2或x=3
(3)解：(2x+3)² - 4(2x+3)=0
(2x+3)[(2x+3)-4]=0
(2x+3)(2x-1)=0
2x+3=0或2x-1=0
∴x=-3/2或x=1/2
(4)解：2(x-3)² - (x²-9)=0
2(x-3)²-(x+3)(x-3)=0
(x-3)[2(x-3)-(x+3)]=0
(x-3)(x-9)=0
x-3=0或x-9=0
∴x=3或x=9