Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMeans / inequalityMedium2 minQB

MathematicsMediumsingle choice

For positive real $a, b, c, d$ with $ab c d = 1$ , find the minimum of $(1 + a) (1 + b) (1 + c) (1 + d)$ .

Answer:

Solution:

AM-GM gives $1 + t \geq 2 t$ for each positive variable $t$ . Multiplying gives a lower bound $16 ab c d = 16$ , attained at $a = b = c = d = 1$ .

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

⏱ 2mℹ️ Source: QB

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