If a,b,c are non-negative real numbers with a^2 \plus{} b^2 \plus{} c^2 \equal{} 1, prove that:
\frac {a}{b^2 \plus{} 1} \plus{} \frac {b}{c^2 \plus{} 1} \plus{} \frac {c}{a^2 \plus{} 1} \geq \frac {3}{4}(a\sqrt {a} \plus{} b\sqrt {b} \plus{} c\sqrt {c})^2 vectorinequalities proposedinequalities