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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMeans / inequalityMedium2 minQB

MathematicsMediumsingle choice

If $ab c d = 1$ where $a, b, c, d$ are positive reals, then the minimum value of $a^{2} + b^{2} + c^{2} + d^{2} + ab + a c + a d + b c + b d + c d$ is

Options:

Answer:

Solution:

A.M. $\geq$ G.M. on these 10 terms: $\frac{sum}{10} \geq ((ab c d)^{5})^{1/10} = 1$ . The minimum value is 10 (at $a = b = c = d = 1$ ).

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

⏱ 2mℹ️ Source: QB

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