Find 3 consecutive numbers where the product of the smaller two numbers in 19 less than the square of the largest number?

Answer is 5, 6, & 7

x = smallest number

y = x + 1

z = x + 2

(x) (y) = z^2 - 19

(x) (x+1) = (x + 2) ^2 - 19

(x^2 + x) = (x^2 + 4x + 4) - 19

x^2 + x = x^2 + 4x + 4 - 19

x^2 term drops out from both sides

x = 4x + - 15

15 = 4x - x

15 = 3x

15/3 = x

x = 5

y = x + 1 = 6

z = x + 2 = 7

Confirm by substituting back in for the variables:

(x) (y) = z^2 - 19

(5) (6) = (7) ^2 - 19

30 = 49 - 19

30 = 30 [OK]