Lahenda sqrt{(x+1)^2+y^2}+sqrt{(x-1)^2+y^2}=2sqrt{2}

$$\sqrt { ( x + 1 ) ^ { 2 } + y ^ { 2 } } + \sqrt { ( x - 1 ) ^ { 2 } + y ^ { 2 } } = 2 \sqrt { 2 }$$

Lahendage ja leidke x (complex solution)

$$\left\{\begin{matrix}x=-\sqrt{3-y^{2}}\text{; }x=\sqrt{3-y^{2}}\text{, }&arg(\sqrt{2\sqrt{3-y^{2}}+4}+\sqrt{-2\sqrt{3-y^{2}}+4})<\pi \\x=-\sqrt{2-2y^{2}}\text{; }x=\sqrt{2-2y^{2}}\text{, }&arg(\sqrt{-y^{2}+2\sqrt{2-2y^{2}}+3}+\sqrt{-y^{2}-2\sqrt{2-2y^{2}}+3})<\pi \text{ and }arg(y^{2}+1)<\pi \text{ and }y\neq -i\text{ and }y\neq i\end{matrix}\right,$$

Lahendage ja leidke y (complex solution)

$$\left\{\begin{matrix}y=-\sqrt{3-x^{2}}\text{; }y=\sqrt{3-x^{2}}\text{, }&arg(\sqrt{2x+4}+\sqrt{4-2x})<\pi \\y=-\frac{\sqrt{4-2x^{2}}}{2}\text{; }y=\frac{\sqrt{4-2x^{2}}}{2}\text{, }&arg(-\frac{x^{2}}{2}+2)<\pi \text{ and }x\neq -2\text{ and }x\neq 2\text{ and }arg(\sqrt{\frac{x^{2}}{2}+2x+2}+\sqrt{\frac{x^{2}}{2}-2x+2})<\pi \end{matrix}\right,$$

Lahendage ja leidke x

$$x=\sqrt{2-2y^{2}}$$

$$x=-\sqrt{2-2y^{2}}\text{, }|y|\leq 1$$

Lahendage ja leidke y

$$y=\frac{\sqrt{4-2x^{2}}}{2}$$

$$y=-\frac{\sqrt{4-2x^{2}}}{2}\text{, }|x|\leq \sqrt{2}$$