已知x²-3xy-28y²=0,求x²+y²/xy的值

题目

已知x²-3xy-28y²=0,求x²+y²/xy的值

答案

解x²-3xy-28y²=0(x-7y)(x+4y)=0当x-7y=0时x=7y∴(x²+y²)/(xy)=(49y²+y²)/(7y²)=50/7当x+4y=0时x=-4y∴(x²+y²)(xy)=(16y²+y²)/(-4y²)=-17/4