What is the sum of the squares of the two consecutive positive even numbers is 52 what is the smaller number?

Answer 1

Let the smaller number be x, then the larger number is x + 2.

x2 + (x + 2)2 = 52 : x2 + x2 + 4x + 4 = 52 : 2x2 + 4x - 48 = 0.

This equation can be factored :-

1) (2x - 8)(x + 6) = 0

2) (x - 4)(2x + 12) = 0

As we are only concerned with the solution when x is positive that this occurs when 2x - 8 or x - 4 = 0 then x = 4.

The smaller number is 4.