If G is the G.M. between x and y , then the value of G 2 − x 2 1 + G 2 − y 2 1 is equal to

G 2 = x y . Then x y − x 2 1 + x y − y 2 1 = x ( y − x ) 1 + y ( x − y ) 1 = x y ( x − y ) − y + x = x y 1 = G 2 1 .

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MathematicsSequence & SeriesMeans / inequalityMedium2 minQB

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If $G$ is the G.M. between $x$ and $y$ , then the value of $\frac{1}{G ^{2} - x ^{2}} + \frac{1}{G ^{2} - y ^{2}}$ is equal to

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Solution:

$G^{2} = x y$ . Then $\frac{1}{x y - x ^{2}} + \frac{1}{x y - y ^{2}} = \frac{1}{x ( y - x )} + \frac{1}{y ( x - y )} = \frac{- y + x}{x y ( x - y )} = \frac{1}{x y} = \frac{1}{G ^{2}}$ .

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:Means / inequality

⏱ 2mℹ️ Source: QB

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