Question

Find three consecutive numbers, the sum of whose squared is 29 more than three times the square of the smallest.

Answer 1

Let the three numbers be x, x+1 and x+2

(x + x+1 + x+2)^2 = 29 + 3(x)^2

(3x + 3)^2 = 29 + 3x^2

9x^2 + 18x + 9 = 3x^2 + 29

Rearranging,

6x^2 + 18x - 20 = 0

Solve for x.