This is LaTeX code:
[latex]
(a_1b_1+a_2b_2)^2\leq (a_1^2+a_2^2)(b_1^2+b_2^2) \iff 2a_1a_2b_1b_2\leq (a_1b_2)^2+(a_2b_1)^2
[/latex]