Question

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

Answer 1

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`.