If \(x + \frac{1}{x} = 2\), then which one of the following is the value of \(x^{32} + \frac{1}{x^{32}}\) ?

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Q: 73 (CAPF/2024)
If \(x + \frac{1}{x} = 2\), then which one of the following is the value of \(x^{32} + \frac{1}{x^{32}}\) ?

question_subject: 

Mathematics

question_exam: 

CAPF

Given \(x + \frac{1}{x} = 2\), \(x = 1\). Therefore, \(x^{32} + \frac{1}{x^{32}} = 1^32 + 1/1^32 = 1\).