已知x²-3xy-28y²=0,求x²+y²/xy的值

已知x²-3xy-28y²=0,求x²+y²/xy的值
已知x²-3xy-28y²=0,求x²+y²/xy的值

已知x²-3xy-28y²=0,求x²+y²/xy的值
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

1-3y/x -28y^2/x^2=0
28y^2/x^2+3y/x-1=0
y/x =(-3+11)/(2*28)=1/7 或(-3-11)/(2*28) =-1/4
所以 (x^2+y^2)/(xy)
=x/y+y/x
=7+1/7=50/7
或=-4-1/4=-17/4