Question

Find three consecutive positive integers such that the square of the first increased by twice the second is three less than four times the third.

Answer 1

3, 4, 5

Explanation:

I like to let x represent the middle integer. Then the first is x-1 and the third is x+1. The given relation is ...

(x-1)^2 +2x = 4(x+1) -3

We can put this equation into standard form and solve.

x^2 -2x +1 +2x = 4x +4 -3

x^2 -4x = 0 . . . . . subtract 4x+1

x(x -4) = 0

So, x=0 is a solution to the equation, but an extraneous solution with respect to the problem.

x = 4 is also a solution to the equation, indicating the integers are 3, 4, 5.

_____

Check

3^2 +2·4 = 4·5 -3

17 = 17 . . . . answer checks OK