Question

the product of two consecutive integers is three less than three times their sum.find the integers.

Answer 1

Let the intergers be x and x + 1, then x(x + 1) = 3(x + x + 1) - 3
x^2 + x = 3(2x + 1) - 3
x^2 + x = 6x + 3 - 3
x^2 - 6x + x = 0
x^2 - 5x = 0
x(x - 5) = 0
x = 0 or x - 5 = 0
x = 0 or x = 5

The integers are 0 and 1 or 5 and 6.