- #1
ElectronicTeaCup
- 23
- 1
- Homework Statement
- $$
\left(x \sqrt{\left(\frac{3+\sqrt{13}}{2 \sqrt{13}}\right)}-y \sqrt{\frac{3-\sqrt{13}}{2 \sqrt{13}}}\right)^{2}-2\left(x \sqrt{\left(\frac{3+\sqrt{13}}{2 \sqrt{13}}\right)-y\left(\frac{3-\sqrt{13}}{2 \sqrt{13}}\right)}\right)\left(x \sqrt{\frac{3-\sqrt{13}}{2 \sqrt{13}}}-y \sqrt{\frac{3+\sqrt{3}}{2 \sqrt{13}}}\right)+4\left(x \sqrt{\frac{3-\sqrt{13}}{2 \sqrt{13}}}-y \sqrt{\frac{3+\sqrt{13}}{2 \sqrt{13}}}\right)^{2}-4=0
$$
- Relevant Equations
- Substituting in second order polynomial to rotate it to remove xy values. But this question is just to ask for a technique for simplifying.
I'm not sure how to simplify this without spending a lot of time on it. Is there a pattern that I need to weed out?
##x^{\prime 2}(5 / 2-\sqrt{13} / 2)+y^{\prime 2}(5 / 2+\sqrt{13} / 2)-4=0##