Question:
If \(x+\frac{1}{x}=4\), find the value of \(x^2+\frac{1}{x^2}\).
If \(x+\frac{1}{x}=4\), find the value of \(x^2+\frac{1}{x^2}\).
Show Hint
You do not have to solve the quadratic for x explicitly, but if you do, notice how the surd terms are designed to cancel out when you add $x^2$ and $\frac{1}{x^2}$.
Updated On: Jul 8, 2026
- 12
- 14
- 16
- 18
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The Correct Option is B
Solution and Explanation
Squaring: \(\left(x+\frac{1}{x}\right)^2=x^2+2+\frac{1}{x^2}=16\). Therefore \(x^2+\frac{1}{x^2}=16-2=14\). Correct option: 14.
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