Question

Find two positive numbers whose sum is 15 and the sum of whose squares is minimum.

Class - 12
AOD

Answer 1

Hope that above image will help you...☺️☺️

Answer 2

Answer: The numbers are 7.5 and 7.5.

Step-by-step explanation:

Let the first number is x,

Since, the sum of two number is 15,

⇒ First number + second number = 15,

⇒ x + second number = 15

⇒ Second number = 15 - x

Let f(x) shows the sum of the squares of the number,

⇒ f(x) = x² + (15-x)² = 2x²- 30x + 225,

By differentiating with respect to x,

We get,

f'(x) = 4x - 30,

For maximum or minimum, f'(x) = 0,

⇒ 4x - 30 = 0 ⇒ x = 7.5,

Again differentiating f'(x) with respect to x,

f''(x) = 4

At x = 7.5 f''(x) = Positive,

Thus, f(x) is minimum at x = 7.5,

Hence, the first number is 7.5,

And, the second number is 15 - 7.5 = 7.5