Question

Evaluate each of the following expressions for x = − 2, y = −1, z = 3:
(i) $\frac{x}{y}+\frac{y}{z}+\frac{z}{x}$
(ii) $x^2+y^2+z^2-xy-yz-zx$

Answer 1

We have x = −2, y = −1 and z = 3.
Thus,
(i)
$$\begin{gathered} \frac{x}{y}+\frac{y}{z}+\frac{z}{x} \\ =\left(\frac{-2}{-1}\right)+\left(\frac{-1}{3}\right)+\left(\frac{3}{-2}\right) \\ =2-\frac{1}{3}-\frac{3}{2} \\ =\frac{12-2-9}{6}=\frac{12-11}{6}=\frac{1}{6} \end{gathered}$$

(ii) x² + y² + z²- xy - yz - zx
= (-2)² + (-1)² + (3)² - (-2)(-1) - (-1)(3) - (3)(-2)
= 4 + 1 + 9 - 2 + 3 + 6
= (4 + 1 + 9 + 3 + 6) - 2
= 23 - 2 = 21