Verified by Ajay Kumar
If \(\sqrt{x}+\frac{1}{\sqrt{x}}=\sqrt{7}\), what is the value of \(x+\frac{1}{x}\)?
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Answer: D
Solution: Squaring both sides, \((\sqrt{x}+\frac{1}{\sqrt{x}})^2=7\). Thus, \(x+2+\frac1x=7\), so \(x+\frac1x=5\). Trick: Use \((a+b)^2=a^2+2ab+b^2\); here the middle term is 2.
यदि \(\sqrt{x}+\frac{1}{\sqrt{x}}=\sqrt{7}\), तो \(x+\frac{1}{x}\) का मान क्या है?
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उत्तर: D
हल: दोनों पक्षों का वर्ग करने पर \((\sqrt{x}+\frac{1}{\sqrt{x}})^2=7\)। इसलिए \(x+2+\frac1x=7\), अतः \(x+\frac1x=5\)। ट्रिक: \((a+b)^2=a^2+2ab+b^2\) का प्रयोग करें; यहाँ मध्य पद 2 है।
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