(a) Let $x$ be a real number with $x \ge 1$. Prove that $x^3 - 5x^2 + 8x - 4 \ge 0$. (b) Let $a, b \ge 1$ real numbers. Find the minimum value of the expression $ab(a + b - 10) + 8(a + b)$. Determine also the real number pairs $(a, b)$ that make this expression equal to this minimum value.
