So i did this last week, and nailed it. The teacher hasn't given it back yet and I was trying to do it again, now I'm stuck.

I need to prove that

$\displaystyle [\dfrac{1}{2}(a+b)] ^2\leq \dfrac{1}{2}(a^2+b^2)$

I do know that the inequality is equivalent to $\displaystyle 0 \leq a^2 -2ab +b^2$