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
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The sum of squares =
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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.
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