$$x + \frac { 1 } { x } = 52 \pi r ( x ^ { 2 } - \frac { 1 } { x } ) = 525$$
$\frac{x^{2}+1}{x}=\frac{52\pi r\left(x^{3}-1\right)}{x}\text{ and }\frac{52\pi r\left(x^{3}-1\right)}{x}=525$
$\left\{\begin{matrix}x=\frac{\sqrt{275621}+525}{2}\text{, }&r=-\frac{525\left(523-\sqrt{275621}\right)}{28610192\pi }\\x=\frac{525-\sqrt{275621}}{2}\text{, }&r=-\frac{525\left(\sqrt{275621}+523\right)}{28610192\pi }\end{matrix}\right.$
$\left\{\begin{matrix}r=-\frac{525\left(\sqrt{275621}+523\right)}{28610192\pi }\text{, }&x=\frac{525-\sqrt{275621}}{2}\\r=-\frac{525\left(523-\sqrt{275621}\right)}{28610192\pi }\text{, }&x=\frac{\sqrt{275621}+525}{2}\end{matrix}\right.$
