# Two numbers have a difference of 20. How do you find the numbers if the sum of their squares is a minimum?

##### 2 Answers

#### Explanation:

Two numbers

The sum of their squares is given by

As we can see,

The numbers are

10 and -10

Solved without Calculus.

#### Explanation:

In Cesareo’s answer

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Let the second number be

Set

This equation is a quadratic and as the

Write as

What follows is part of the process for completing the square.

Consider the 20 from

Thus the first number is

The second number is