The sum of the squares of two consecutive positive even numbers is 52. Find the numbers.
The sum of the squares of two consecutive positive even numbers is 52. Find the numbers.
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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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