Question

已知m^2=m+1 n^2=n+1且m不等于n求下列各式的值①m+n②mn

Answer 1

m^2-n^2=(m+n)(m-n)=m-n,所以m+n=1

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