Question

Find three consecutive positive integers such that sum of their square is 149.

Answer 1

Let the three consecutive positive integers be

x − 1, x, x + 1

(x − 1)² + x² + (x + 1)² = 149

(x² − 2x + 1) + x² + (x² + 2x + 1) = 149

3x² + 2 = 149

3x² = 147

x² = 49

x = 7

The three consecutive positive integers are:

6, 7, 8​