I need to show the binary quadratic forms $5x^2+xy+y^2$ and $x^2-xy+5y^2$ are equivalent. We've only touched on quadric forms, and the only definition I have for "equivalence" is that one can be transformed into the other via a substitution:
$x = px' +qy', \hspace{15mm}y=rx'+sy'$
with $ps-qr=1$. How can I find such a substitution? Or is there a way to do this without actually having to find the substitution itself?
Thank you guys for any insight into this. This is getting beyond what I can keep in my head