Question

If \(x + \dfrac{1}{x} = 5\), then the value of \(x^2 + \dfrac{1}{x^2}\) is:

• A. 23
• B. 25
• C. 27
• D. 21

Answer 1

The Correct Option is A

Step 1: Square both sides: \(\left(x+\dfrac1x\right)^2 = x^2 + 2 + \dfrac{1}{x^2} = 25\).
Step 2: So \(x^2 + \dfrac{1}{x^2} = 25 - 2 = 23\).

Quick Tip: \(x^2+\tfrac1{x^2} = (x+\tfrac1x)^2 - 2\).