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Solve the Following Question and Mark the Best Possible Option. If X, Y, Z Are Positive Real Numbers, Such that X + Y + Z = 25, Then the Maximum Value of 1/X + 1/Y + 1/Z is - Mathematics

MCQ

Solve the following question and mark the best possible option.
If x, y, z are positive real numbers, such that x + y + z = 25, then the maximum value of `1/x + 1/y + 1/z` is

Options

  • `9/25`

  • `12/31`

  • `4/25`

  • 1

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Solution

We have AM ≥ HM

⇒ `( x + y + z)/3 ≥ 3/(1/x + 1/y + 1/z) `

⇒ `1/x + 1/y + 1/z ≥ 9/25`

Hence minimum value of `1/x + 1/y + 1/z "is" 9/25`.

Concept: Number System (Entrance Exam)
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