Question

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

Answer 1

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.