已知x+y=6,xy=-2,求(x^4-y^4)÷(6x-6y)的值.
问题描述:
已知x+y=6,xy=-2,求(x^4-y^4)÷(6x-6y)的值.
答
(x^4-y^4)÷(6x-6y)
=(x^2-y^2)(x^2+y^2)÷[(x+y)(x-y)]
=x^2+y^2
=(x+y)^2-2xy
=6^2-2×(-2)
=36+4
=40