Question

若m^2=m+1,n^2=n+1,且m不等于n,求代数式m^3+n^3的值

Answer 1

m^2=m+1,n^2=n+1,m不等于n

即m,n为一元二次方程x²-x-1=0的两个根

m+n=1

mn=-1

m^3+n^3=m²m+n²n=m²+m+n²+n=2(m+n+1)=4