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.