解方程 (mx-n)²=(nx-m)² (m²≠n²)

解方程 (mx-n)²=(nx-m)² (m²≠n²)
解方程 (mx-n)²=(nx-m)² (m²≠n²)

解方程 (mx-n)²=(nx-m)² (m²≠n²)
m²x²－2mnx＋n²＝n²x²－2mnx＋m²
﹙m²－n²﹚x＝m²－n²
x＝1

(mx-n)²=(nx-m)²
(mx-n)²-(nx-m)² =0
(mx-n+nx-m)(mx-n-nx+m)=0
[(m+n)x-(m+n)][(m-n)x-(m-n)]=0
(m+n)(x-1)(m-n)(x-1)=0
(m²≠n²)
所以m+n≠0 m-n≠0 所以x-1=...

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(mx-n)²=(nx-m)²
(mx-n)²-(nx-m)² =0
(mx-n+nx-m)(mx-n-nx+m)=0
[(m+n)x-(m+n)][(m-n)x-(m-n)]=0
(m+n)(x-1)(m-n)(x-1)=0
(m²≠n²)
所以m+n≠0 m-n≠0 所以x-1=0 x=1

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(mx-n)²=(nx-m)²
去括号化简得（m^2-n^2)x^2=（m^2-n^2
m²≠n²，x^2=1
x=±1