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