Question

已知x+y=1/2,xy=-1/3,求(x四次方-y四次方)÷x二次方+y二次方/xy÷（6x-6y）

Answer 1

x+y=1/2,xy=-1/3
(x四次方-y四次方) ÷ (x二次方+ y二次方)/(xy)÷（6x-6y）
= (x四次方-y四次方) × xy/ (x二次方+ y二次方) × 1/(6x-6y）
= (x二次方+ y二次方) (x+y)(x-y) × xy /(x二次方+y二次方) × 1/[6(x-y)]
= (x+y) × xy
= 1/2 × (-1/3)
= -1/6

Answer 2

解：已知x+y=1/2,xy=-1/3,
(x四次方-y四次方)÷x二次方+y二次方/xy÷（6x-6y）
=（x^4-y^4)/(x^2+y^2/(xy)/(6x-6y)
=(x^4-y^4)*xy/(x^2+y^2)*1/[6(x-y)]
=(x^2-y^2)xy/[6(x-y)]
=(x+y)xy/6
=1/2*(-1/3)/6
=-1/6/6
=-1/36