Question

m平方等于m+1,n平方等于n+1,且m不等于n.求m5次方+n5次方的值

Answer 1

m²=m+1,m²-m-1=0

n²=n+1,n²-n-1=0

m不等于n

所以m和n是方程x²-x-1=0的两个跟

所以m+n=1,mn=-1

m²+n²=(m+n)²-2mn=1+2=3

m³+n³=(m+n)(m²-mn+n²)=1*(3+1)=4

所以m^5+n^5=(m²+n²)(m³+n³)-m³n²-m²n³

=3*4-(mn)²(m+n)

=12-(-1)²*1

=11