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The sum of the squares of two consecutive even numbers is 6500. Which is the smaller number?

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The sum of the squares of two consecutive even numbers is 6500. Which is the smaller number?
(a) 54 (b) 52
(c) 48 (d) 56
(e) None of these

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(d) Let the two numbers be x and (x + 2). 

Then, x2 + (x + 2)2 = 6500 

x2 + x2 + 4x + 4 = 6500 

2x2 + 4x – 6496 = 0 

x2 + 2x – 3248 = 0 

x2 + 58x – 56x – 3248 = 0 

(x + 58) (x – 56) = 0 

x = 56

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