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If (u=\sqrt{13}+\sqrt{5}) and (v=\sqrt{13}-\sqrt{5}), what is the value of (\frac{u^{2}-v^{2}}{uv})?यदि (u=\sqrt{13}+\sqrt{5}) और (v=\sqrt{13}-\sqrt{5}), तो (\frac{u^{2}-v^{2}}{uv}) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (2\sqrt{65})(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}).(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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