# Parametric Equation Problem

• July 13th 2012, 11:37 AM
Telo
Parametric Equation Problem
x^2-6xy+10y^2=4

find all the integer pairs of x and y which satisfiy the equation.

Thanks!
• July 13th 2012, 01:00 PM
a tutor
Re: Parametric Equation Problem
You can solve for x and then choose y values that give integer values of x.
• July 13th 2012, 02:51 PM
skeeter
Re: Parametric Equation Problem
Quote:

Originally Posted by Telo
x^2-6xy+10y^2=4

find all the integer pairs of x and y which satisfiy the equation.

Thanks!

$x^2 - 6xy + 10y^2 - 4 = 0$

$a = 1$ , $b = -6y$ , $c = 10y^2 - 4$

the quadratic formula yields ...

$x = 3y \pm \sqrt{4 - y^2}$

since x is an integer value, the value under the radical must be a positive, perfect square value ... finish it.