Question

If x + y + z = 9 and xy + yz + zx = 23, then the value of (x³ + y³ + z³ − 3xyz) = ?
(a) 108
(b) 207
(c) 669
(d) 729

Answer 1

(a) 108

$x^3+y^3+z^3-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)$
$$\begin{gathered} =\left(x+y+z\right)\left[{\left(x+y+z\right)}^2-3\left(xy+yz+zx\right)\right] \\ =9\times \left(81-3\times 23\right) \\ =9\times 12 \\ =108 \end{gathered}$$