15问答网 > 已知x⼀5=y⼀3,则x⼀x+y+y⼀x-y-y^2⼀x^2+y^2的值为？ O(∩_∩)O谢谢

已知x⼀5=y⼀3,则x⼀x+y+y⼀x-y-y^2⼀x^2+y^2的值为？ O(∩_∩)O谢谢

2024-12-09 05:30:07

推荐回答（1个）

回答1：

已知x/5=y/3那么y=3x/5
x/(x+y)+y/(x-y)-y²/(x²+y²)
=［(x²-xy)(x²+y²)+(xy+y²)(x²+y²)-y²(x²-y²)］/［(x²-y²)(x²+y²)］
=(x^4+x²y²-x³y-xy³+x³y+xy³+y²x²+y^4-y²x²+y^4)/(x^4-y^4)
=(x^4+x²y²+2*y^4+y^4)/(x^4-y^4)
=［x^4+x²(3/5*x)²+2*(3/5*x)^4］/［x^4-(3/5*x)^4)］
=［x^4+x²(3/5*x)²+2*(3/5*x)^4］/［x^4-(3/5*x)^4)］
=(x^4+9/25*x^4+162/625*x^4)/(x^4-81/625*x^4)
=［x^4(625+225+162)/625］/［x^4(625-81)/625］
=1012/544
=253/136