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If \(x-\frac{1}{x}=6\), what is the value of \(x^{2}+\frac{1}{x^{2}}\)?
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Answer and explanation
Correct answer: (38)
We use \(\left(x-\frac{1}{x}\right)^{2}=x^{2}+\frac{1}{x^{2}}-2\). Thus \(36=x^{2}+\frac{1}{x^{2}}-2\), so the value is (38).
Frequently asked questions
What is the correct answer to this question?
(38)
Why is this the correct answer?
We use \(\left(x-\frac{1}{x}\right)^{2}=x^{2}+\frac{1}{x^{2}}-2\). Thus \(36=x^{2}+\frac{1}{x^{2}}-2\), so the value is (38).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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