If $a,b,c $ are the lengths of the edges of a triangle, show that:
$$\frac {6 (a^2+b^2+c^2)}{a+b+c}\geq \frac {(a+b)^2}{b+c}+\frac {(b+c)^2}{a+c}+\frac {(c+a)^2}{a+b} $$
I have no idea how to start.
If $a,b,c $ are the lengths of the edges of a triangle, show that:
$$\frac {6 (a^2+b^2+c^2)}{a+b+c}\geq \frac {(a+b)^2}{b+c}+\frac {(b+c)^2}{a+c}+\frac {(c+a)^2}{a+b} $$
I have no idea how to start.
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