(九年级上二次根式习题)已知x≠y,x2+√2y=√3,y2+√2x=√3,求xy的值.

题目

(九年级上二次根式习题)已知x≠y,x2+√2y=√3,y2+√2x=√3,求xy的值.

答案

两式相除得 （x2+√2y）/(y2+√2x)=1
x2+√2y=y2+√2x
(x+y)*(x-y)=+√2(x-y)
x+y=√2
(x+y)2=x2+y2+2xy
2=√3-√2y+√3-√2x+2xy
2=2√3-√2(x+y)+2xy
2=2√3-2+2xy
xy=2-√3