Question

用因式分解法解下列方程。要过程

①（x-2)²-2（x-2)=0
②25x²-4=0
③（x-2)²-9=0
④x²+2x-8=0

Answer 1

解：
①（x-2)²-2（x-2)=0
（x-2)(x-2-2)=0
（x-2)(x-4)=0
x-2=0,x-4=0
x₁=2, x₂=4
②25x²-4=0

(5x)²-2²=0
(5x+2)(5x-2)=0
5x+2=0, 5x-2=0
x₁=-2/5, x₂=2/5
③（x-2)²-9=0
（x-2)²-3²=0
(x-2+3)(x-2-3)=0
(x+1)(x-5)=0
x+1=0, x-5=0
x₁=-1, x₂=5
④x²+2x-8=0
(x-2)(x+4)=0
x-2= 0, x+4=0
x₁=2, x₂=-4

愿对你有所帮助！

Answer 2

1. （X-2)(X-2-2)=0     X1-2=0  .......   X1=0

   X2-2-2=0  .......     X2=4

2. (5X+2)*(5X-2)=0     5X1+2=0........ X1=-2/5

   5X2-2=0...............X2=2/5

3. (X-2+3)*(x-2-3)=0     x1-2+3=0..........x1=-1

   x2-2-3=0...........x2=5

4. (x+4)*(x-2)=0

   x+4=0.......x1=-4

   x-2=0        x2=2

Answer 3

解
16x²=(x-2)²
(x-2)²-16x²=0
(x-2)²-(4x)²=0
(x-2-4x)(x-2+4x)=0
(-3x-2)(5x-2)=0
∴x=2/5或x=-2/3

3x(x-1)=2-2x
3x(x-1)=-2(x-1)
3x(x-1)+2(x-1)=0
(3x+2)(x-1)=0
x=1或x=-2/3

(m+2)(2m-5)=-10
2m²-m-10+10=0
2m²-m=0
m(2m-1)=0
∴m=0或m=1/2