Giải thích các bước giải:
$M=x^2+2y^2-x-2y-xy$
$=x^2-x(y+1)+\dfrac{(y+1)^2}{4}+2y^2-2y-\dfrac{(y+1)^2}{4}$
$=(x-\dfrac{y+1}{2})^2+\dfrac{7y^2-10y-1}{4}$
$=(x-\dfrac{y+1}{2})^2+\dfrac{7}{4}.\left(y-\dfrac{5}{7}\right)^2-\dfrac{8}{7}$
$\ge\dfrac{-8}7$
$\to Min_M=\dfrac{-8}7$
$\to (x-\dfrac{y+1}{2})^2=7\left(y-\dfrac{5}{7}\right)^2=0$
$\to x=\dfrac 67,y=\dfrac 57$