Question

\(x = \;\sqrt[3]{{121\;\sqrt[3]{{121\;\sqrt[3]{{121 \ldots \ldots \ldots \infty }}}}}}\), then find the value of 11x^-1.
1. 11
2. 121
3. 1
4. 0

Answer 1

Correct Answer - Option 3 : 1

Given:

\(x = \;\sqrt[3]{{121\;\sqrt[3]{{121\;\sqrt[3]{{121 \ldots \ldots \ldots \infty }}}}}}\)

Explanation:

On cubing both sides we get,

x³ = 121x

∵ \(x = \;\sqrt[3]{{121\;\sqrt[3]{{121\;\sqrt[3]{{121 \ldots \ldots \ldots \infty }}}}}}\)

⇒ x² = 121

⇒ x = 11

11x^-1 = 11 × (1/x)

⇒ 11 × (1/11)

∴ The value of 11x^-1 is 1.