Question

若m为正实数,且m的平方-m-1=0,则m的平方-1/m的平方=?

Answer 1

m²-m-1=0m-1-1/m=0m-1/m=1,(m-1/m)²=1m²+1/m²=3(m+1/m)²=5,∵m>0,∴m+1/m=√5,∴(m²-1/m²)=(m+1/m)(m-1/m)=√5×1=√5.