Problems Section: Problems 1201 - 1210

Q1201 Let $x_1$ and $x_2$ be the solutions of
$$ x^2 - (a+d)x + ad - bc = 0.$$
Prove that $x_1^3$ and $x_2^3$ are the solutions of
$$x^2 - (a^3 + d^3 + 3abc + 3bcd)x + (ad-bc)^3 = 0.$$