Which expression will be obtained in the numerator when the denominator of \(\frac{1}{3-\sqrt{5}}\) is rationalised?\(\frac{1}{3-\sqrt{5}}\) के हर को परिमेय बनाने पर अंश में कौन-सा व्यंजक प्राप्त होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(3+\sqrt{5}\)\(3+\sqrt{5}\)
The conjugate of \(3-\sqrt{5}\) is \(3+\sqrt{5}\). Therefore, multiply the numerator and denominator by \(3+\sqrt{5}\): \(\frac{1}{3-\sqrt{5}}\times\frac{3+\sqrt{5}}{3+\sqrt{5}}=\frac{3+\sqrt{5}}{9-5}=\frac{3+\sqrt{5}}{4}\). Hence, the new numerator is \(3+\sqrt{5}\). Remember that the conjugate is formed by changing only the sign between the two terms; \(8\) is not the denominator, since \(9-5=4\).हर \(3-\sqrt{5}\) का संयुग्मी \(3+\sqrt{5}\) होता है। इसलिए अंश और हर दोनों को \(3+\sqrt{5}\) से गुणा करते हैं: \(\frac{1}{3-\sqrt{5}}\times\frac{3+\sqrt{5}}{3+\sqrt{5}}=\frac{3+\sqrt{5}}{9-5}=\frac{3+\sqrt{5}}{4}\)। अतः नया अंश \(3+\sqrt{5}\) है। ध्यान रखें, संयुग्मी में केवल बीच का चिह्न बदलता है।
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