Đáp án:
Ta có:
`2x^2-3xy+y^2`
`=2x^2-2xy-xy+y^2`
`=2x(x-y)-y(x-y)`
`=(x-y)(2x-y)`
\(\begin{cases}2x^2-3xy+y^2+x-y=0\\x^2+2x-y=2\\\end{cases}\)
`<=>` \(\begin{cases}(2x-y)(x-y)+x-y=0\\x^2+2x-y=2\\\end{cases}\)
`<=>` \(\begin{cases}(x-y)(2x-y+1)=0\\x^2+2x-y=2\\\end{cases}\)
`<=>` \(\begin{cases}\left[ \begin{array}{l}x=y\\2x-y+1=0\end{array} \right.\\x^2+2x-y=2(1)\\\end{cases}\)
`**x=y`
`(1)<=>x^2+2x-x=2`
`<=>x^2+x-2=0`
`<=>` \(\left[ \begin{array}{l}x=y=-2\\x=y=1\end{array} \right.\)
`**2x-y+1=0`
`<=>y=2x+1`
`(1)<=>x^2+2x-2x-1=2`
`<=>x^2-1=2`
`<=>x^2=3`
`<=>` \(\left[ \begin{array}{l}x=\sqrt3\\x=-\sqrt3\end{array} \right.\)
`<=>` \(\begin{cases}\left[ \begin{array}{l}x=\sqrt3\\y=2x+1=2\sqrt3+1\end{array} \right.\\\left[ \begin{array}{l}x=-\sqrt3\\y=2x+1=1-2\sqrt3\end{array} \right.\\\end{cases}\)
Vậy HPT có 4 nghiệm `(x,y) in {(1,1),(-2,-2),(sqrt3,2sqrt3+1),(-sqrt3,1-2sqrt3)`.