If $$x = \frac{a}{b} + \frac{b}{a},\,y = \frac{b}{c} + \frac{c}{b}$$     and $$z = \frac{c}{a} + \frac{a}{c},$$   then what is the value of xyz - x² - y² - z²?

A. -4

B. 2

C. -1

D. -6

Answer: Option A

Solution(By Examveda Team)

Let a = b = c = 1
∴ x = 2, y = 2, z = 2
xyz - x² - y² - z²
= 2 × 2 × 2 - 4 - 4 - 4
= 8 - 12
= -4