Question

m^2=n+2,n^2=m+2(m不等于n),求m^3-2mn+n^3的值

m^2=n+2,n^2=m+2(m不等于n),求m^3-2mn+n^3的值
大家知道请告诉怎么做好吗？谢谢了```

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

n＝m^2－2，n^2＝m^4-4m^2+4＝m+2
m^4-4m^2-m+2＝0＝(m+1)(m-2)(m^2+m-1)=0
当n≠m,m≠2 且 m≠-1,所以m^2+m-1，同理n^2+n-1=0
m^3-2mn+n^3＝m*m^2-2mn+n*n^2=m(n+2)-2mn+n(m+2)=2(m+n)
n≠m,所以m n 是方程x^2+x-1＝0的两根，m+n＝-1
原式＝-2

Answer 3

解:根据m^2=n+2,n^2=m+2(m不等于n),得:
m^2-n^2=n-m
又因为m^2-n^2=(m-n)(m+n),
所以m+n=-1

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