Proving homogenous quadratic inequalities Okay, I'm having trouble proving this:
$$5x^2-4xy+6y^2 \ge 0, \text{ where } x,y \in \mathbb{R}$$
I have tried a few values of $x$ and $y$ and I find that is true. EX: $x=y=0$ which make the equation $= 0$
I have tried factoring it but i find that the factors will involve imaginary numbers.
So i would like a way to prove this inequality.

$$
5x^2-4xy+6y^2 = 2(x-y)^2 + 3x^2 + 4y^2,
$$
where each term is non-negative
