Question 5
The nonnegative real numbers $a$ and $b$ satisfy $a + b = 1$. Prove that
$$
\frac{1}{2} \le \frac{a^3 + b^3}{a^2 + b^2} \le 1.
$$
When do we have equality in the left inequality, and when in the right one?
$$
\frac{1}{2} \le \frac{a^3 + b^3}{a^2 + b^2} \le 1.
$$
When do we have equality in the left inequality, and when in the right one?