Prove $(a + b)^2 \geq 4ab$
What direction should I take with this proof? Can I use induction here? or is there a better method?
I tried a few manipulations, but couldn't seem to find a form that proved it for all $x$.
One such manipulation resulted in:
$a^2 + b^2 \geq 2ab$
which seems close to the triangle inequality. Can I use this somehow?