SOLUTION: Can you help me with this problem? Find two consecutive positive even integers whose sum of their squares is 6500.

Question 755522: Can you help me with this problem? Find two consecutive positive even integers whose sum of their squares is 6500.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
x^2 + (x+2)^2 = 6500

x^2 + x^2 + 4x + 4 = 6500

2x^2 + 4x + 4 = 6500

2x^2 + 4x + 4 - 6500 = 0

2x^2 + 4x - 6496 = 0

Use the quadratic formula to solve for x

Plug in , ,

or

or

or

or

x = 56

x + 2 = 56 + 2 = 58

So the two consecutive positive even integers are 56 and 58.
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