Find the three consecutive odd numbers whose sum of the squares is 2531.

Question: Find the three consecutive odd numbers whose sum of the squares is 2531.Solution:Let three consecutive odd numbers be x, x + 2, x + 4.x2 + (x + 2)2 + (x + 4)2 = 2531Simplifying we get,⇒ x2 + 4x - 837=0⇒ x2 + 31x - 27x - 837=0 [ 27 × 31 = 837 and also the difference between 27 and 31 is 4 ]⇒ (x + 31) (x - 27)⇒ x = 27 or x = - 31Hence, the value ofx = 27(x + 2) = 27 + 2 = 29(x + 4) = 27 + 4 = 31