Question

The sum of two non-zero numbers is 6. The minimum value of the sum of their reciprocals is ______.

विकल्प

• `3/4`

• `6/5`

• `2/3`

• None of these

Answer 1

The sum of two non-zero numbers is 6. The minimum value of the sum of their reciprocals is `2/3`.

Explanation:

Let x + y = 6

⇒ y = 6 – x

`1/x + 1/y = (x + y)/(xy)`

f(x) = `6/(xy) = 6/(x(6 - x)) =6/(6x - x^2)`

∴ f'(x) = `(-6)/(6x - x^2)^2 * (6 - 2x)`

For maximum or minimum of f(x),

f'(x) = 0

⇒ 6 – 2x = 0

∴ x = 3 and y = 3

∴ `"min"(1/x + 1/y) = 1/3 + 1/3 = 2/3`