Question

解方程(m^2-n^2)x^2-4mnx=m^2-n^2 (m^2不等于n^2)求x

Answer 1

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

Answer 2

(m^2-n^2)x^2-4mnx=(m^2-n^2)
(m^2-n^2)x^2-4mnx-(m^2-n^2)=0
(m+n)(m-n)x^2-4mnx-(m+n)(m-n)=0
用十字相乘：
[(m+n)x+(m-n)]*[(m-n)x-(m+n)]=0
x1=-(m-n)/(m+n)
x2=(m+n)/(m-n)
有不懂欢迎追问

Answer 3

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

因为(m+n)^2-(m-n)^2=0

所以原方程可分解为
[(m+n)x+(m-n)]*[(m-n)x-(m+n)]=0

x=(n-m)/(m+n)
或(m+n)/(n-m)
祝你学习愉快！