Prove this function is strictly convex

Question

I need to understand how to prove a function of this form is strictly convex:

Let $f \colon \mathbb{R}^3 \rightarrow \mathbb{R}$ be defined by:

$f(x) = 2x_1^2 + 3x_2^2 + x_3^2$.

Prove by using the definition, i.e. $f(\lambda + (1-\lambda)b) < \lambda f(a) + (1-\lambda)f(b)$, that $f$ is strictly convex.

Thank you in advance for any answer that might help explaining the procedure

Answer 1

Ok found a solution, the problem can be solved by using $2xy < x^2 + y^2$, because x is not equal to y.