Question
Download Solution PDFयदि \(x = {{\sqrt5 - \sqrt4} \over {\sqrt5 + \sqrt4}}\) और \(y = {{\sqrt5 + \sqrt4} \over {\sqrt5 - \sqrt4}}\) फिर \(x^2 - xy + y^2 \over x^2 +xy + y^2\) = ? का मान ज्ञात करें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया:
\(x = {{\sqrt5 - \sqrt4} \over {\sqrt5 + \sqrt4}}\) और \(y = {{\sqrt5 + \sqrt4} \over {\sqrt5 - \sqrt4}}\)
गणना:
प्रश्न के अनुसार,
\(x = {{\sqrt5 - \sqrt4} \over {\sqrt5 + \sqrt4}}\)
⇒x = 9 - 4√5
⇒x² = 161 - 72√5
और \(y = {{\sqrt5 + \sqrt4} \over {\sqrt5 - \sqrt4}}\)
⇒y = 9 + 4√5
⇒y² = 161 + 72√5
अब,
\(x^2 - xy + y^2 \over x^2 +xy + y^2\)
= (161 - 72√5 - 1 + 161 + 72√5)/(161 - 72√5 + 1 + 161 + 72√5)
= (322 - 1)/(322 + 1)
= 321/323
इसलिए, अपेक्षित मान 321/323 है।
Last updated on Jun 9, 2025
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