Giải thích các bước giải:
$6x^2+10y^2+2xy-x-28y+18=0$
$\to 6x^2+x(2y-1)+10y^2-28y+18=0$
$\to \Delta =(2y-1)^2-4.6(10y^2-28y+18)=-236y^2+668y-431$
$\to\Delta\ge 0$
$\to -236y^2+668y-431\ge 0$
$\to 236y^2-668y+431\le 0$
$\to 236(y-\dfrac{167}{118})^2\le \dfrac{2460}{59}$
$\to -\dfrac{\sqrt{615}}{59}+\dfrac{167}{118}\le y\le \dfrac{\sqrt{615}}{59}+\dfrac{167}{118}$
$\to 1\le y\le 1\to y=1$
$\to 6x^2+10+2x-x-28+18=0$
$\to 6x^2+x=0$
$\to x=0, x\in Z$
