Question

If x + 1/x = 5, what is the value of x² + 1/x²?

• A. 21
• B. 23
• C. 17
• D. 19

Answer 1

The Correct Option is B

Given: \[ x + \frac{1}{x} = 5 \] Square both sides: \[ \left(x + \frac{1}{x}\right)^2 = 5^2 = 25 \] Apply the identity \[ \left(x + \frac{1}{x}\right)^2 = x^2 + \frac{1}{x^2} + 2 \] Therefore, \[ x^2 + \frac{1}{x^2} = 25 - 2 = \boxed{23} \]