题目

已知:x^2+y^2+6x-8y+25=0,求(x/x^2-y^2)÷y/(y-x)

提问时间：2021-03-02

答案

x²+y²+6x-8y+25=0
(x²+6x+9)+(y²-8y+16)=0
(x+3)²+(y-4)²=0
x+3=0,y-4=0
x=-3,y=4
x/(x²-y²)÷y/(y-x)
=x/[(x+y)(x-y)]×(y-x)/y
=-x/[y(x+y)]
=3/[4×(-3+4)]
=3/4