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If (x=2+\sqrt{7}), what is the value of (x+\frac{1}{x})?
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Answer and explanation
Correct answer: (2\sqrt{7})
(\frac{1}{2+\sqrt{7}}) equals (\frac{2-\sqrt{7}}{-3}=\frac{\sqrt{7}-2}{3}). So (x+\frac{1}{x}=2+\sqrt{7}+\frac{\sqrt{7}-2}{3}=\frac{4+4\sqrt{7}}{3}).
Frequently asked questions
What is the correct answer to this question?
(2\sqrt{7})
Why is this the correct answer?
(\frac{1}{2+\sqrt{7}}) equals (\frac{2-\sqrt{7}}{-3}=\frac{\sqrt{7}-2}{3}). So (x+\frac{1}{x}=2+\sqrt{7}+\frac{\sqrt{7}-2}{3}=\frac{4+4\sqrt{7}}{3}).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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