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Question
The sum of the squares of two consecutive positive even numbers is 52. Find the numbers.
Solution
Let the consecutive positive even numbers be x and x + 2.
From the given information,
x2 + (x + 2)2 = 52
2x2 + 4x + 4 = 52
2x2 + 4x – 48 = 0
x2 + 2x – 24 = 0
(x + 6)(x – 4) = 0
x = – 6, 4
Since, the numbers are positive, so x = 4.
Thus, the numbers are 4 and 6.
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