Question 80
Let $a$, $b$, $c$ be positive real numbers such that $a + b + c = a^{2} + b^{2} + c^{2}$. Show that
$$
\frac{a^{2}}{a^{2} + ab} + \frac{b^{2}}{b^{2} + bc} + \frac{c^{2}}{c^{2} + ca} \geq \frac{a + b + c}{2}
$$
$$
\frac{a^{2}}{a^{2} + ab} + \frac{b^{2}}{b^{2} + bc} + \frac{c^{2}}{c^{2} + ca} \geq \frac{a + b + c}{2}
$$