{2x^2-xy-y^2-x=3,2x-3y=1,求xy

题目

{2x^2-xy-y^2-x=3,2x-3y=1,求xy
xy就是x.y

答案

2x²-3xy+2xy-y²-x=3
x(2x-3y)+2xy-y²-x=3
2x-3y=1
所以x+2xy-y²-x=3
2xy-y²=3
2x=3y+1
所以2xy=3y²+y
所以3y²+y-y²=3
2y²+y-3=0
(y-1)(2y+3)=0
y=1,y=-3/2
2x=3y+1
所以x=2,x=-7/4
所以xy=2或21/8