Question 155
Denote by $a$, $b$ and $c$ the sides of a triangle, opposite the angles $\alpha$, $\beta$ and $\gamma$, respectively. If $\alpha$ is sixty degrees, show that
$$
a^{2} = \frac{a^{3} + b^{3} + c^{3}}{a + b + c}.
$$
$$
a^{2} = \frac{a^{3} + b^{3} + c^{3}}{a + b + c}.
$$