Question

Given, x + 1/x = 4 find the value of x³ + 1/x³.

• A. 55
• B. 57
• C. 52
• D. 50

Answer 1

Answer:

C. 52

Given:
$x + \frac{1}{x} = 4$
Cube both sides using identity

$\left(x + \frac{1}{x}\right)^3 = x^3 + \frac{1}{x^3} + 3\left(x + \frac{1}{x}\right)$

Substitute value 4:
$4^3 = x^3 + \frac{1}{x^3} + 3(4)$
$64 = x^3 + \frac{1}{x^3} + 12$

Solve

$x^3 + \frac{1}{x^3} = 64 - 12 = 52$

Answer:

$\boxed{52}$