SOLUTION: The sum of two numbers is 33. The sum of the squares of these numbers is 557. Find the two numbers.

Question 1188743: The sum of two numbers is 33. The sum of the squares of these numbers is 557. Find the two numbers.
Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
Make two equations:

x + y = 33
x² + y² = 557

From the first equation, let: y = 33 - x

Substitute y = 33 - x into the second equation:

x² + (33 - x)² = 557

Simplify and solve for x:

x² + (1089 - 66x + x²) = 557

2x² - 66x + 1089 = 557

2x² - 66x + 532 = 0

x² - 33x + 266 = 0

(x - 14)(x - 19) = 0

x = 14; x = 19

There are two solutions. If you let x = 14 and substitute this into the original first equation (x + y = 33), this means y = 19.

And, if you let x = 19 and substitute this into the original first equation (x + y = 33), this means y = 14.

Either way, the two numbers you are looking for are 14 and 19.
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