CMR : $x^{2}$ + $y^{2}$ + x + y + 3 > 0

`x^2 + y^2 + x + y + 3`

`= x^2 + 2 . x . 1/2 + (1/2)^2 + y^2 + 2 . y . 1/2 + (1/2)^2 - 1/4 - 1/4 + 3`

`= (x + 1/2)^2 + (y + 1/2)^2 + 5/2`

$\text{Ta có : $(x + \dfrac{1}{2})^{2}$ ≥ 0 ∀ x ; $(y + \dfrac{1}{2})^{2}$ ≥ 0 ∀ y}$

$\text{=> $(x + \dfrac{1}{2})^{2}$ + $(y + \dfrac{1}{2})$ + $\dfrac{5}{2}$ > 0 ∀ x,y}$

$\text{Vậy $x^{2}$ + $y^{2}$ + x + y + 3 > 0 ∀ x,y}$