Rešite x-y=sqrt{2}xy=1

$$x-y= \sqrt{ 2 } xy=1$$

Ovrednoti (complex solution)

$$x-y=\sqrt{2}xy\text{ and }\sqrt{2}xy=1$$

Rešitev za x

$$\left\{\begin{matrix}x=\frac{\sqrt{2\sqrt{2}+1}}{2\left(2\sqrt{2}-1\right)}-\frac{\sqrt{4\sqrt{2}+2}}{2\sqrt{2}-1}+\frac{\sqrt{2}}{2\sqrt{2}-1}-\frac{1}{2\left(2\sqrt{2}-1\right)}\text{, }&y=\frac{-\sqrt{2\sqrt{2}+1}-1}{2}\\x=\frac{\sqrt{4\sqrt{2}+2}}{2\sqrt{2}-1}-\frac{\sqrt{2\sqrt{2}+1}}{2\left(2\sqrt{2}-1\right)}+\frac{\sqrt{2}}{2\sqrt{2}-1}-\frac{1}{2\left(2\sqrt{2}-1\right)}\text{, }&y=\frac{\sqrt{2\sqrt{2}+1}-1}{2}\end{matrix}\right,$$

Rešitev za y

$$\left\{\begin{matrix}y=\frac{\sqrt{2\sqrt{2}+1}}{2\left(2\sqrt{2}-1\right)}-\frac{\sqrt{4\sqrt{2}+2}}{2\sqrt{2}-1}-\frac{\sqrt{2}}{2\sqrt{2}-1}+\frac{1}{2\left(2\sqrt{2}-1\right)}\text{, }&x=\frac{-\sqrt{2\sqrt{2}+1}+1}{2}\\y=\frac{\sqrt{4\sqrt{2}+2}}{2\sqrt{2}-1}-\frac{\sqrt{2\sqrt{2}+1}}{2\left(2\sqrt{2}-1\right)}-\frac{\sqrt{2}}{2\sqrt{2}-1}+\frac{1}{2\left(2\sqrt{2}-1\right)}\text{, }&x=\frac{\sqrt{2\sqrt{2}+1}+1}{2}\end{matrix}\right,$$