x^2-6xy+3y^2=100 x,y are natural numbers.

Help would be appreciated.

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- Sep 14th 2013, 08:36 PMRuyHayabusax,y equation
x^2-6xy+3y^2=100 x,y are natural numbers.

Help would be appreciated. - Sep 15th 2013, 12:44 AMBobPRe: x,y equation
Use the usual formula to solve as a quadratic in x.

You need the term under the square root sign to be a perfect square. - Sep 15th 2013, 01:46 AMtopsquarkRe: x,y equation
To add to bobP's comment, once you get your expression for a perfect square you are likely to need to use a spreadsheet to find the x values. At least I could find no pattern for the first 5 perfect squares.

-Dan - Sep 16th 2013, 02:16 AMBobPRe: x,y equation
Wolfram Alpha gives a complete set of integer solutions. They look quite messy and I haven't checked them out in any way.

The first few though are not difficult following the quadratic/discriminant route.

You need $\displaystyle 6y^{2}+100$ to be a square, so check out the sequence $\displaystyle 6y^{2}=21, 44, 69, 96,...$ .

$\displaystyle 6y^{2}=96$ gets you an early hit and a second comes not much further on. - Sep 16th 2013, 04:28 PMtopsquarkRe: x,y equation
I may have been using a more complicated system than you. (I had to define a z that was equal to the square root of the discriminant.) This is a rather common difficulty of mine. :)

How did you code your question to Wolfram|Alpha? I tried to do that to check my work but was unable to get it to solve the problem

-Dan - Sep 17th 2013, 01:32 AMBobPRe: x,y equation
I'm not a regular user of Wolfram Alpha, in fact this is the first time that I've actually asked it a question.

I simply typed in the equation and pressed the compute button.

It came back with a whole pile of stuff, including a graph, which was pleasing to see, and a section headed 'Integer Solutions '.