Problem

Source: Iran 2005

Tags: inequalities, 3-variable inequality, cyclic inequality, cauchy schwarz



Suppose $a,b,c\in \mathbb R^+$. Prove that :\[\left(\frac ab+\frac bc+\frac ca\right)^2\geq (a+b+c)\left(\frac1a+\frac1b+\frac1c\right)\]