Question 155016
(x+1)^3-x^3=217
x^3+3x^2+3x+1-x^3=217
3x^2+3x-216=0
(3x-24)(x+9)=0
3x-24=0
3x=24
x=24/3
x=8 for the amallernteger.
8+1=9 for the larger integer.
proof;
9^3-8^3=217
729-512=217
217=217