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Class 10MathematicsPolynomialsOperations on real numbers and the laws of exponentsExpert
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If \(y=7+4\sqrt{3}\), what is the value of \(y+\frac{1}{y}\)?

Answer and explanation

Correct answer: \(14\)

Since \((7+4\sqrt{3})(7-4\sqrt{3})=49-48=1\), we get \(\frac{1}{7+4\sqrt{3}}=7-4\sqrt{3}\). Therefore, \(y+\frac{1}{y}=(7+4\sqrt{3})+(7-4\sqrt{3})=14\). Exam tip: For expressions of the form \(a+b\sqrt{c}\), use the conjugate \(a-b\sqrt{c}\) to rationalise the denominator.

Related tags

RationalizationConjugatesSurdsReal NumbersOperations On Real Numbers And The Laws Of ExponentsPolynomialsMathematicsClass 10 Mcq
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