Question 437040
x = one number
y = a number that is one less than x
y = x-1
.
The sum of squares =
{{{x^2 + (x-1)^2 = x^2 + x^2 -2x + 1}}}
{{{x^2 + x^2 -2x + 1 = 2x^2 -2x + 1}}}
.
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:
{{{graph(500,500,-10,10,-10,10,2*x*x - 2*x + 1)}}}
We immediately see this is a parabola and that the minimum value occurs when x = 1/2.
Checking this value we find:
{{{2x^2 -2x + 1 = 2(1/4) -2(1/2) + 1}}}
{{{2(1/4) -2(1/2) + 1 = 1/2 -1 + 1}}}
{{{1/2 -1 + 1 = 1/2}}}
Looking back at the question it asks for two numbers
{{{x = 1/2}}}
{{{x-1 = -1/2}}}
What is their sum of their squares?
{{{1/4 + 1/4 = 1/2}}}
That fits with our graph, too.
Answer: The two numbers are 1/2 and -1/2.
Done.