Question 314850
Find three consecutive numbers where the product of the smallest two numbers is 28 less than the square of the largest numbers.
.
Let x = smallest of three consecutive numbers
then
x+1 = middle number
x+2 = largest number
.
(x+1)(x+2) = x^2 - 28
x^2+2x+x+2 = x^2 - 28
x^2+3x+2 = x^2 - 28
3x+2 = -28
3x = -30
x = -3 (smallest number)
.
middle:
x+1 = -3+1 = -2 (middle)
.
Largest number:
x+2 = -3+2 = -1 (largest)
.
solution, -3, -2, -1