Why is this inequality true? $(a+b)^2\leq 2(a^2+b^2)$ Why is this inequality true? $a,b$ are real numbers.
$$
(a+b)^2=a^2+2ab+b^2\leq 2(a^2+b^2)
$$
I know $(a+b)^2=a^2+2ab+b^2 \geq 0$, but then?

Because by C-S $$2(a^2+b^2)=(1^2+1^2)(a^2+b^2)\geq(1\cdot a+1\cdot b)^2=(a+b)^2$$
