SOLUTION: The sum of the squares of two numbers which differ by 3 is equal to 549. Find the numbers.

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Question 629902: The sum of the squares of two numbers which differ by 3 is equal to 549. Find the numbers.
Answer by Charles3475(23) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the first number.

The second number would then be x + 3

The sum of the squares would then be:

x%5E2+%2B+%28x%2B3%29%5E2+=+549 (Given)

x%5E2+%2B+x%5E2+%2B+6x+%2B+9+=+549 (Expand terms)

2x%5E2+%2B+6x+-+540+=+0 (Subtract 549 from both sides and Add like terms)

x%5E2+%2B+3x+-+270+=+0 (Divide both sides by 2)

%28x%2B18%29%2A%28x-15%29+=+0 (Factor the equation)

Either (x+18) = 0 or (x-15) = 0

x equals -18 or 15 (Solve for x)

There are two pairs of numbers that work (-18, -15) and (15, 18)