यदि \(u=\sqrt{13}+\sqrt{5}\) और \(v=\sqrt{13}-\sqrt{5}\), तो \(\frac{u^{2}-v^{2}}{uv}\) का मान क्या है?
If \(u=\sqrt{13}+\sqrt{5}\) and \(v=\sqrt{13}-\sqrt{5}\), what is the value of \(\frac{u^{2}-v^{2}}{uv}\)?
Explanation opens after your attempt
Correct Answer
B. \(2\sqrt{65}\)
Concept
Here (u^{2}-v^{2}=(u-v)(u+v)=2\sqrt{5}\cdot2\sqrt{13}=4\sqrt{65}) and (uv=8). Hence the value is \(\frac{\sqrt{65}}{2}\).
Why this answer is correct
The correct answer is B. \(2\sqrt{65}\). Here (u^{2}-v^{2}=(u-v)(u+v)=2\sqrt{5}\cdot2\sqrt{13}=4\sqrt{65}) and (uv=8). Hence the value is \(\frac{\sqrt{65}}{2}\).
Exam Tip
(u^{2}-v^{2}=(u-v)(u+v)=2\sqrt{5}\cdot2\sqrt{13}=4\sqrt{65}) और (uv=8)। इसलिए मान \(\frac{\sqrt{65}}{2}\) है।
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