Question

If \( x + \frac{1}{x} = 2 \) and \( x \) is a real number, then the value of \( x^{17} + \frac{1}{x^{17}} \) is:

• A. 4
• B. -2
• C. 2
• D. 0

Hint:

Always test simple values like \( x = 1 \) or \( x = -1 \) when dealing with symmetric equations like \( x + \frac{1}{x} \).

Answer 1

The Correct Option is C

We are given: \( x + \frac{1}{x} = 2 \).
Let us assume \( x = 1 \). Then, \( x + \frac{1}{x} = 1 + 1 = 2 \) which satisfies the condition.
Now we compute \( x^{17} + \frac{1}{x^{17}} \).
Since \( x = 1 \), we have \( x^{17} + \frac{1}{x^{17}} = 1 + 1 = 2 \).