# 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

#### 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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