$\text{Giải thích các bước giải:}$
$A = x² - xy + y² - 2x - 2y$
$A = (x² + \dfrac{1}{4}y² + 1 - xy - 2x + y) + 3(\dfrac{1}{4}y² - y + 1) - 4$
$A = (x - \dfrac{1}{2}y - 1)² + 3(\dfrac{1}{2}y - 1)² - 4$
$\text{Do}$ $(x - \dfrac{1}{2}y - 1)² + 3(\dfrac{1}{2}y - 1)² ≥ 0$
$⇔ (x - \dfrac{1}{2}y - 1)² + 3(\dfrac{1}{2}y - 1)² - 4 ≥ -4$
$⇔ A ≥ -4$
$\text{Dấu "=" xảy ra ⇔}$ $\left \{ {{y = 2} \atop {x - \frac{1}{2}y =
1}} \right.$
$⇔ \left \{ {{y=2} \atop {x=2}} \right.$
$\text{Vậy Min A = -4 ⇔ x = y = 2}$
$\huge\text{Hk tốt !}$
