jasperE3 wrote: If $a,b,c$ are the sides and $\alpha,\beta,\gamma$ the corresponding angles of a triangle, prove the inequality $$\frac{\cos\alpha}{a^3}+\frac{\cos\beta}{b^3}+\frac{\cos\gamma}{c^3}\ge\frac3{2abc}.$$ $$\iff$$$$\frac{b^2+c^2}{a^2}+\frac{c^2+a^2}{b^2}+\frac{a^2+b^2}{c^2}\geq 6$$