Let $ a, b, c$ be positive real numbers such that $ bc +ca +b = 1,$ . Prove that $$ \frac {1 +b^2c^2}{(b +c)^2} + \frac {1+ c^2a^2}{(c + a)^2} +\frac {1 +a^2b^2}{(a +b)^2} \geq \frac {5}{2}.$$
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Tags: inequalities, 6th edition
Let $ a, b, c$ be positive real numbers such that $ bc +ca +b = 1,$ . Prove that $$ \frac {1 +b^2c^2}{(b +c)^2} + \frac {1+ c^2a^2}{(c + a)^2} +\frac {1 +a^2b^2}{(a +b)^2} \geq \frac {5}{2}.$$