Question

The two parts of 120 for which the sum of double of first and square of second part is minimum, are ______.

Options

• 60, 60

• 119, 1

• 118, 2

• None of these

Answer 1

The two parts of 120 for which the sum of double of first and square of second part is minimum, are 119, 1.

Explanation:

Let one number be (120 – x) and then another is x.

∴ f(x) = `2(120 - x) + x^2`

= `x^2 - 2x + 240`

∴ f(x) = 0

⇒ 2x – 2 = 0

⇒ x = 1

Here, f''(x) = 2 > 0

Therefore function is minimum at x = 1.

So the numbers are 119 and 1.