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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMeans / inequalityMedium2 minQB

MathematicsMediumsingle choice

If $b$ is the arithmetic mean of positive $a, x$ , geometric mean of positive $a, y$ , and harmonic mean of positive $a, z$ , find $x yz$ .

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Answer:

Solution:

From $b = (a + x) /2, b^{2} = a y$ , and $b = 2 a z / (a + z)$ , we obtain $x = 2 b - a, y = b^{2} / a$ , and $z = ab / (2 a - b)$ . Therefore $x yz = b^{3} (2 b - a) / (2 a - b)$ .

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

⏱ 2mℹ️ Source: QB

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