Question

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

Answer 1

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]