已知2/x+2/y=根号24,求 x/y(x-y) - y/x(x-y)的值

题目

已知2/x+2/y=根号24,求 x/y(x-y) - y/x(x-y)的值

答案

2/x+2/y=根号24
(2y+2x)/xy=2√6
x+y=xy√6
x/y(x-y) - y/x(x-y)
=1/(x-y)[(x/y-y/x)]
=1/(x-y)[(x²-y²)/xy]
=1/(x-y)[(x-y)(x+y)/xy]
=(x+y)/xy
=xy√6/xy
=√6