SOLUTION: Find two consecutive even natural numbers such that the sum of their squares is 340 .

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Question 960867: Find two consecutive even natural numbers such that the sum of their squares is 340 .
Answer by Theo(13342) About Me  (Show Source):
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the two consecutive numbers are x and x + 2.
x^2 + (x+2)^2 = 340
simplify to get:
x^2 + x^2 + 4x + 4 = 340
combine like terms to get:
2x^2 + 4x + 4 = 340
subtract 340 from both sides to get:
2x^2 + 4x - 336 = 0
factor out the 2 to get:
x^2 + 2x - 168 = 0
factor the quadratic to get:
(x-12) * (x+14) = 0
x is equal to 12.
x + 2 is equal to 14.
x^2 + (x+2)^2 is equal to 12^2 + 14^2 which is equal to 340.