Let the numbers be x, x + 1 and x + 2.
From the information given:-
x(x + 1)(x + 2) = x^3 + 85
Solving for x:-
x(x^2 + 3x + 2) = x^3 + 85
x^3 + 3x^2 + 2x = x^3 + 85
3x^2 + 2x - 85 = 0
3x^2 - 15x + 17x - 85 = 0
3x(x - 5) + 17(x - 5) = 0
(3x + 17)(x - 5) = 0
x = -17/3 , 5
We take x = 5 because x is an integer.
Answer:- the 3 integers are 5, 6 and 7.
