Find two consecutive natural numbers whose cubes differ by 61

Question

Find two consecutive natural numbers whose cubes differ by 61. what the quadratic equation?

Answer 1

Let the smaller number be $a$

$\implies 61=(a+1)^3-a^3=3a^2+3a+1$

Can you simplify to form the required Quadratic Equation?

Answer 2

Quite easy to be honest.

You start from: .

Expanding (x+1)^3 and reducing the equation to normal form you get: , which is a simple quadratic equation you should be able to solve (otherwise look it up on your book or here http://mathworld.wolfram.com/QuadraticEquation.html).

This is the graph of the equation.

Edit: I've just seen you asked a few questions on problems involving quadratic equations, so this is an unrequested advice for you: re-read you coursebook (both "theory" and worked problems) and give a shoot to some other problems. Also, you can have a look at this video http://www.youtube.com/watch?v=nAdVUXsMQe4 , which seems quite good.