已知实数x,y满足x2+(根号2)*y=根号3,y2+(根号2)x=根号3且x≠y,求xy的值
问题描述：
已知实数x,y满足x2+(根号2)*y=根号3,y2+(根号2)x=根号3且x≠y,求xy的值
答
两式做差,有
x^2+√2y-y^2-√2x=0
即(x-y)(x+y-√2)=0
而x≠y,x-y≠0
故x+y=√2
两式求和,有
x^2+√2y+y^2+√2x=2√3
(x+y)^2-2xy+√2(x+y)=2√3
xy=2-√3最后一步、、跳得太快了。x+y=√2带入就行了.....