解方程组(x+y)(x-2y)=-5 (x-y)(x+2y)=7
问题描述：
解方程组(x+y)(x-2y)=-5 (x-y)(x+2y)=7
答
(x+y)(x-2y)=-5
(x-y)(x+2y)=7
x^2-xy-2y^2=-5
x^2+xy-2y^2=7
两式相加得：x^2-2y^2=1
两式相减得：xy=6
x=6/y代入x^2-2y^2=1
得:x=-3,y=-2
答
展开
x^2-2y^2-xy=-5
x^2-2y^2+xy=7
所以
x^2-2y^2=1
xy=6
上式除以下式,解分式方程
x/y=3/2或-4/3(舍去)
所以 x^2=9 y^2=4
x=3 y=2
或x=-3 y=-2