`2x^2 - 3xy + 2y^2 = m(x - y)^2 + n(x + y)^2`
`<=> 2x^2 - 3xy + 2y^2 = m(x^2 - 2xy + y^2) + n(x^2 + 2xy + y^2)`
`<=> 2x^2 - 3xy + 2y^2 = mx^2 - m. 2xy + my^2 + nx^2 + n. 2xy + ny^2`
`<=> 2x^2 - 3xy + 2y^2 = (mx^2 + nx^2) + (-m. 2xy + n. 2xy) + (my^2 + ny^2)`
`<=> 2x^2 - 3xy + 2y^2 = (m + n)x^2 - (2m - 2n)xy + (m + n)y^2`
`<=>` \(\left\{\begin{matrix}m + n = 2\\2m - 2n = 3\end{matrix}\right.\)
`<=>` \(\left\{\begin{matrix}m + n = 2\\2(m - n) = 3\end{matrix}\right.\)
`<=>` \(\left\{\begin{matrix}m + n = 2\\m - n = 1,5\end{matrix}\right.\)
`<=>` \(\left\{\begin{matrix}m = (2 + 1,5) : 2 = 1,75\\n = 2 - 1,75 = 0,25\end{matrix}\right.\)
Vậy `x = 1,75; n = 0,25`
