SOLUTION: The sum of two numbers is 14. The sum of the squares of the two numbers is 106. Find the two numbers.

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Question 394694: The sum of two numbers is 14. The sum of the squares of the two numbers is 106. Find the two numbers.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

The sum of two numbers is 14

Let x and (14-x) represent the two numbers

Question states***

 x^2 + (14-x)^2 = 106

solving for x

  2x^2 -28x + 196 = 106

  2x^2 -28x + 90 = 0 

 2(x^2 -14x + 45) = 0

factoring

  (x-9)(x-5) = 0  Numbers are 5 and 9



CHECKING our Answer***

 25 + 81 = 106