SOLUTION: The difference of two numbers is 1. What is the smallest possible value for the sum of their squares? Find the numbers.

Question 437040: The difference of two numbers is 1. What is the smallest possible value for the sum of their squares? Find the numbers.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
x = one number
y = a number that is one less than x
y = x-1
.
The sum of squares =

.
Assuming you mean 'integers' when you say 'numbers', then we could try some values:
When x = 0, the sum of squares = 1
When x = -1, the sum of squares = 4
When x = 1, the sum of squares = 1
...
But randomly plugging in values of x and checking the sum is not a very mathematical approach.
Instead, let's look at the graph:

We immediately see this is a parabola and that the minimum value occurs when x = 1/2.
Checking this value we find:

Looking back at the question it asks for two numbers

What is their sum of their squares?

That fits with our graph, too.
Answer: The two numbers are 1/2 and -1/2.
Done.
RELATED QUESTIONS
The difference of two positive numbers is 1 and the sum of their squares is 61. Find the... (answered by kevwill)

The difference of two numbers is 2. If the difference of their squares is 18, what is (answered by checkley79)

find two numbers such that their sum multiplied by the sum of their squares is 5500, and... (answered by oscargut)

The sum of two numbers is 25, and the difference of their squares is 75. What are the two (answered by Paul)

find two numbers whose sum is 13 and the difference of their squares is... (answered by srinivas.g)

the sum of two numbers is 16 and their difference is 5. find the difference of their... (answered by mananth)

The sum of two numbers is 30 and their difference is 6. Find the difference of their... (answered by ikleyn)

The sum of two numbers is 8 and the difference between their squares is 34. Find their... (answered by rakhileshnaidu,Alan3354)