$\quad x^2 + x + 1$
$= x^2 + 2\cdot\dfrac12x + \dfrac14 + \dfrac34$
$=\left(x +\dfrac12\right)^2 +\dfrac34$
Ta có:
$\quad \left(x +\dfrac12\right)^2\geq 0\quad \forall x \in\Bbb R$
$\to \left(x +\dfrac12\right)^2 +\dfrac34 > 0\quad \forall x \in\Bbb R$
Vậy $x^2 + x + 1 > 0 \quad \forall x \in\Bbb R$
