Question

m^2=n+2,n^2=m+2(m不等于n),求m^3-2mn+n^3的值

因为m^2=n+2,n^2=m+2 所以 m^2-n^2=n-m 即 (m-n)(m+n)=n-m m+n=1
为什么得m+n=1，求详解。

Answer 1

因为m^2=n+2,n^2=m+2
所以 m^2-n^2=n-m
即 (m-n)(m+n)=-(m-n)
m+n=-1

m^3-2mn+n^3=m·m^2-2mn+n·n^2
=m(n+2)-2mn+n(m+2)
=mn+2m-2mn+mn+2n
=2(m+n)
因为m+n=-1 所以 原式=-2

Answer 2

(m-n)(m+n)=n-m
(m-n)(m+n+1)=0
m+n=-1

m^2=n+2,n^2=m+2
m^2+n^2=n+2+m+2
(m+n)^2-2mn=4-1
1-2mn=3
mn=-1

m^3-2mn+n^3=（m+n)^3-3m^2n-3n^2m-2mn=-1-3mn(m+n)-2mn=-1+mn=-2

Answer 3

应该是：m+n=-1

Answer 4

1