Løs p=(q-n)(q+n)/n^2-2

$$p = \frac { ( q - n ) ( q + n ) } { n ^ { 2 } - 2 }$$

Løs for n

$$\left\{\begin{matrix}n=\sqrt{\frac{2p+q^{2}}{p+1}}\text{; }n=-\sqrt{\frac{2p+q^{2}}{p+1}}\text{, }&|q|\neq \sqrt{2}\text{ and }\left(p<-1\text{ or }p\geq -\frac{q^{2}}{2}\right)\text{ and }\left(p>-1\text{ or }p\leq -\frac{q^{2}}{2}\right)\text{ and }p\neq -1\\n\in \mathrm{R}\setminus \sqrt{2},-\sqrt{2}\text{, }&p=-1\text{ and }|q|=\sqrt{2}\end{matrix}\right,$$

Løs for p

$$p=-\frac{n^{2}-q^{2}}{n^{2}-2}$$

$$|n|\neq \sqrt{2}$$