Question

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

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