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Numbers System — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsNumbers 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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