Question

用两种方法解方程(x-2)2-9(x+1)2=0

括号后是平方,写下2种方法过程,谢谢~~

Answer 1

(x-2)2-9(x+1)2=0
1. ((x-2)+3(x+1))*((x-2)-3(x+1))=0
解,得:x=-1/4或x=-5/2
2. (x^2-4x＋4)-9(x^2+2x+1)=0
8x^2+22x+5=0
解,得:x=-1/4或x=-5/2

Answer 2

解法一
原式等于：[（X-2）+3（X+1）][（X-2）-3（X+1）]=0
（X-2）+3（X+1）=0或（X-2）-3（X+1）=0
X=-1/4或X=-5/2
解法二
原式等于：X2-4X+4-9（X2+2X=1）=0
8X2+22X+5=0
X=-1/4或X=-5/2

Answer 3

(x-2)^2-9(x-1)^2=0
=>(x-2+3x-3)(x-2-3x+3)=0
=>(4x-5)(-2x+1)=0
=>x=5/4或x=1/2
(x-2)^2-9(x-1)^2=0
=>x^2-4x+4-9(x^2-2x+1)=0
=>-8x^2+14x-5=0
=>8x^2-14x+5=0
=>(4x-5)(2x-1)=0
=>x=5/4或x=1/2

Answer 4

1.打开括号算
2.移到等号两边,开方