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Rationalise the denominator and find the value of \(\frac{1}{2-\sqrt{3}}\).हर को परिमेय बनाकर \(\frac{1}{2-\sqrt{3}}\) का मान निकालिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(2+\sqrt{3}\)\(2+\sqrt{3}\)
Multiply by the conjugate \(2+\sqrt{3}\):
\[\frac{1}{2-\sqrt{3}}\cdot\frac{2+\sqrt{3}}{2+\sqrt{3}}=\frac{2+\sqrt{3}}{(2-\sqrt{3})(2+\sqrt{3})}\]
Denominator is a difference of squares:
\[(2-\sqrt{3})(2+\sqrt{3})=2^2-(\sqrt{3})^2=4-3=1\]
So the value is \(2+\sqrt{3}\).सहसंयुग्मी (conjugate) \(2+\sqrt{3}\) से गुणा करें:
\[\frac{1}{2-\sqrt{3}}\cdot\frac{2+\sqrt{3}}{2+\sqrt{3}}=\frac{2+\sqrt{3}}{(2-\sqrt{3})(2+\sqrt{3})}\]
हर एक वर्गों के अंतर के रूप में है:
\[(2-\sqrt{3})(2+\sqrt{3})=2^2-(\sqrt{3})^2=4-3=1\]
इसलिए मान \(2+\sqrt{3}\) है।
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