SOLUTION: find two consecutive even numbers if the sum of their squares is 100.

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Question 478485: find two consecutive even numbers if the sum of their squares is 100.
Answer by amoresroy(361) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the first even number
x + 2= the second even number
x^2 + (x+2)^2 = 100
x^2 + x^2 + 4x +4 = 100
2x^2 + 4x -96 = 0
Divide by 2 to get
x^2 + 2x -48 = 0
Solve for x by factoring
(x-6)(x+8)= 0
x = 6
x+2 = 8
The two consecutive even numbers are 6 and 8.
To check
6*6 + 8*8 = 36 + 64 = 100