Maharashtra BoardEnglish MediumSTD 9MathsNumber System2 Marks
Question
Write the reciprocal of $\big(2+\sqrt{3}\big).$
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Answer
The reciprocal of $\big(2+\sqrt{3}\big)$$=\frac{1}{2+\sqrt{3}}$
$=\frac{1}{2+\sqrt{3}}\times\frac{2-\sqrt{3}}{2-\sqrt{3}}$
$=\frac{2-\sqrt{3}}{2^2-\big(\sqrt{3}\big)^2}$
$=\frac{2-\sqrt{3}}{4-3}$
$=2-\sqrt{3}$
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