Question

已知m的平方等于m+n,n的平方等于m+2,求m立方+2mn+n立方的值

Answer 1

m^2=m+2,

n^2=n+2,m≠n,

∴m,n是x^2-x-2=0的两根,

∴m+n=1,mn=-2,

m^3+2mn+n^3

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

=m^2+mn+n^2

=(m+n)^2-mn

=1+2=3.