You can only solve for x in terms of y or vice versa (and you can use the quadratic formula in this case)
To solve for x and y you need another equation
Whenever I'm confronted with a question bearing the label of 'find all solutions' I almost never know how to solve it algebraically (apologies if I spelt that incorrectly), I always have to resort to manual methods, which usually are a bore and I know that is not the true mathematical way to solve them.
Now I've been shown this equation:
x^2+y^2+x+y=1001
and I have to find all integer solutions.
I have no idea of how to solve this because I think the left half of the equation cannot be simplified (or I simply do not know of the method). Until necessary, I'll refrain from using the calculator so please could anyone help me?
~Cyfer
If then , and so . Now 2003 is a prime that is congruent to 3 mod 4 (or in everyday language, it leaves a remainder 3 when divided by 4). It is known (see for example here) that an integer can only be expressed as a sum of two squares if each of its prime factors that is congruent to 3 mod 4 occurs to an even power. That is not the case with 4006, which therefore cannot be expressed as a sum of two squares. So there are no integer solutions (x,y) to your equation.
EDIT: Sorry didn't see the previous post before I wrote this. Will create a reply for the previous post when ready. Apologies.
Surely it would go to 4002 and not 4004 because the two left over 1s from the factorising are positive, so they become negative when brought over.