The sum of the cubes of two numbers is $2071$, while the sum of the two numbers themselves is $19$. Find the two numbers.
I've been working hard to solve this problem and I need someone to tell me how to solve it, it perplexes me.
I know the answer is $7$ and $12$ and it might have something to do with $$a^3 + b^3 = (a + b)(a^2 – ab + b^2)$$ but how do they get to that answer?
Any help will be appreciated thank you.
I followed this Yahoo question up to where it said solve it then I searched like $4$ hours looking for a way to solve it, so I'm hoping someone can help me out.