已知m的平方等于n+2,n的平方等于m+2(m不等于n),求m的平方+2mn+n的平方

Question

如题所述

Answer 1

答案是1.
解题方法如下：
m2 = n+2 (1)
n2 = m+2 (2)
m2-n2 = n - m
(m-n)(m+n) = n - m
m+n = -1
将m,n代入m2+2mm+n2 = (m+n)2
算出来等于1

Answer 2

m^2=n+2
n^2=m+2
两式相减
m^2-n^2=n-m
m≠n,n-m≠0
m+n=-1
m^2+2mn+n^2=(m+n)^2=1

Answer 3

m的平方+2mn+n的平方=(m+n)^2=1
m^2-n^2=n-m
(m+n)(m-n)=-(m-n)
m+n=-1

Answer 4

两式一减，m+n=1
结果为1