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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMeans / inequalityMedium2 minQB

MathematicsMediumsingle choice

Statement 1: If $a, b, c, d > 0$ and $(a + b + c + d + 3)^{5} = 9375 ab c d$ , then $a + b + c + d = 12$ . Statement 2: Equality in the arithmetic-mean/geometric-mean inequality for positive numbers holds only when all numbers are equal.

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Answer:

Solution:

Apply AM-GM to $a, b, c, d, 3 : (a + b + c + d + 3)^{5} \geq 5^{5} \cdot 3 ab c d = 9375 ab c d$ . Equality forces $a = b = c = d = 3$ , so their sum is 12.

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

⏱ 2mℹ️ Source: QB

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