यदि \(x = {{\sqrt5 - \sqrt4} \over {\sqrt5 + \sqrt4}}\) और \(y = {{\sqrt5 + \sqrt4} \over {\sqrt5 - \sqrt4}}\) फिर \(x^2 - xy + y^2 \over x^2 +xy + y^2\) = ? का मान ज्ञात करें।

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 2)

Answer 1

दिया 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।

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