If x² - 5x + 1 = 0, then the value of x³ + 1/x³ is:

Given: $x^{2} - 5x + 1 = 0$

Step 1: Divide both sides by $x$ (note $x \neq 0$ since the constant term is $1 \neq 0$).

$\frac{x^{2}}{x} - \frac{5x}{x} + \frac{1}{x} = \frac{0}{x}$

$x - 5 + \frac{1}{x} = 0$

Step 2: Isolate the target expression.

$x + \frac{1}{x} - 5 = 0$

$x + \frac{1}{x} = 5$

Answer: 3) 5

5