Q25
ArithmeticAlgebra, Equations & Operations
If $x + \frac{1}{x} = -1$, $x^3 - 1 = ?$
- a.0
- b.1
- c.−1
- d.2
Answer: (A) 0
$x + \frac{1}{x} = -1$ gives $x^2 + x + 1 = 0$. Since $x^3 - 1 = (x - 1)(x^2 + x + 1)$, it equals 0. The values 1, −1 and 2 ignore this factorisation.