Question

计算(1-x)^2=x-1

(1-x)^2=x-1

x^2－2mx＋m^2＝n^2

(m^2－n^2)x^2－4mnx＝m^2－n^2(m^2－n^2不等于0)

Answer 1

(1-x)^2=x-1
(x-1)^2-(x-1)=0
(x-1)(x-1-1)=0
(x-1)(x-2)=0
x=1 或 x=2

x^2－2mx＋m^2＝n^2
(x-m)^2=n^2
(x-m)^2-n^2=0
(x-m+n)(x-m-n)=0
x=m-n 或 x=m+n

(m^2－n^2)x^2－4mnx＝m^2－n^2(m^2－n^2不等于0)
(m^2－n^2)x^2－4mnx-(m^2－n^2)=0
x^2-4mn/(m^2－n^2)-1=0
x^2-4mn/(m^2－n^2)+[2mn/(m^2－n^2)]^2-[2mn/(m^2－n^2)]^2-1=0
[x-2mn/(m^2－n^2)]^2-[4m^2n^2+m^4+n^4-2m^2n^2]/(m^2－n^2)^2=0
[x-2mn/(m^2－n^2)]^2-[m^4+n^4+2m^2n^2]/(m^2－n^2)^2=0
[x-2mn/(m^2－n^2)]^2-[m^2+n^2]^2/(m^2－n^2)^2=0
[x-2mn/(m^2－n^2)+(m^2+n^2)/(m^2－n^2)][x-2mn/(m^2－n^2)-(m^2+n^2)/(m^2－n^2)]=0

[x+(m^2-2mn+n^2)/(m^2－n^2)][x-(m^2+2mn+n^2)/(m^2－n^2)]=0
[x+(m-n)^2/(m^2－n^2)][x-(m+n)^2/(m^2－n^2)]=0
x=-(m-n)^2/(m^2－n^2) 或 x=(m+n)^2/(m^2－n^2)
x=-(m-n)/(m+n) 或 x=(m+n)/(m－n)

(m^2－n^2)x^2－4mnx-(m^2－n^2)=0
[(m+n)x+(m-n)][(m-n)x-(m+n)]=0
x=-(m-n)/(m+n) 或 x=(m+n)/(m－n)

Answer 2

1.分x-1是否为0
x=1或2
2. x-m的绝对值=n的绝对值
讨论n的正负
n大于0 x=m+n或m-n
n小于0 x=m-n或m+n
所以结果为 x=m+n或m-n
3.变形等式有
(mx-n）^2=(nx+m)^2
得到 (mx-n-nx-m)(mx-n+nx+m）=0
得到x=（m+n）/(m-n) 或(n-m)/(m+n)