Prove that $x^2 + 5xy+7y^2 \ge 0$ for all $x,y \in\mathbb{R}$ This is probably really easy for all of you, but my question is how do I prove that $x^2 + 5xy+7y^2 \ge 0$ for all $x,y\in\mathbb{R}$
Thanks for the help!

$$x^2+5xy+7y^2=\left(x+\frac{5y}2\right)^2 + \frac{3y^2}4\ge 0$$
(not $>0$ as $x=y=0$ leads to 0).
