If a , b , c are positive numbers, then least value of ( a + b + c ) ( a 1 + b 1 + c 1 ) is

AM ≥ HM ⇒ 3 a + b + c ≥ a 1 + b 1 + c 1 3 ⇒ ( a + b + c ) ( a 1 + b 1 + c 1 ) ≥ 9

Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesMeans / inequalityMedium2 minPYQ_2020

MathematicsMediumsingle choice

If $a, b, c$ are positive numbers, then least value of $(a + b + c) (\frac{1}{a} + \frac{1}{b} + \frac{1}{c})$ is

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Answer:

Solution:

$AM \geq HM$ $\Rightarrow \frac{a + b + c}{3} \geq \frac{3}{\frac{1}{a} + \frac{1}{b} + \frac{1}{c}}$ $\Rightarrow (a + b + c) (\frac{1}{a} + \frac{1}{b} + \frac{1}{c}) \geq 9$

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

⏱ 2mℹ️ Source: PYQ_2020

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