If \({\rm x} + \frac{1}{{\rm x}} = 2\), then the value of \({{\rm x}^{57}} + \frac{1}{{{{\rm x}^{57}}}}\) is:

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Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 4)

Answer 1

Calculations:

\({\rm x} + \frac{1}{{\rm x}} = 2\),

⇒x² + 1 = 2x

⇒x² - 2x + 1 = 0

⇒(x - 1)² = 0

⇒x = 1

so, \({{\rm x}^{57}} + \frac{1}{{{{\rm x}^{57}}}}\)

= (1)⁵⁷ + 1/(1)⁵⁷

= 1 + 1 = 2

Hence, The Required value is 2.

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