Question

Difference between cubes of two consecutive number is 1 more than 3 times their product. Verify with an example.

Answer 1

Let the numbers be x and x+1 (since numbers are consecutive number one will be x and other will exceed 1 by x)
(x+1)^3 - x^3 = 1+ 3x(x+1)
Example:(1,2)
X=1.X+1=2
2^3-1^3=8-1=7
1+3*1*2=1+6=7