Question

已知x方+y方=3，xy=-(1/2).求(1/x-1/y)÷x方-y方/xy的值

已知x方+y方=3，xy=-(1/2).求(1/x-1/y)÷x方-y方/xy的值

Answer 1

(x+y)²=x²+y²+2xy=2
x+y=±√2

(1/x-1/y)÷x方-y方/xy
=[(y-x)/xy]÷[(x+y)(x-y)/xy]
=(y-x)÷[(x+y)(x-y)]
=-(x-y)÷[(x+y)(x-y)]
=-1/(x+y)
=-1/(±√2)
=±√2/2