Question

用两种方法解方程(x-2)2-9(x-1)2=0

括号后是平方,写2种方法还有过程,谢谢~~

Answer 1

(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