Ratkaise y=sqrt{x+1}-sqrt{1-x}

$$y = \sqrt { x + 1 } - \sqrt { 1 - x }$$

Ratkaise muuttujan x suhteen (complex solution)

$$x=-\frac{\sqrt{y^{2}\left(4-y^{2}\right)}}{2}$$

$$x=\frac{\sqrt{y^{2}\left(4-y^{2}\right)}}{2}\text{, }|-arg(-y)+arg(-\sqrt{x+1}+\sqrt{1-x})|<\pi \text{ and }|arg(-\sqrt{y^{4}-4y^{2}+4})-arg(\frac{y^{2}}{2}-1)|<\pi$$

Ratkaise muuttujan x suhteen

$$\left\{\begin{matrix}x=\frac{y\sqrt{4-y^{2}}}{2}\text{, }&\left(y\leq 0\text{ and }\frac{-\sqrt{2y\sqrt{4-y^{2}}+4}+\sqrt{-2y\sqrt{4-y^{2}}+4}}{2}\geq 0\text{ and }y\geq -\sqrt{2}\text{ and }-y\sqrt{4-y^{2}}\leq 2\right)\text{ or }\left(y\geq 0\text{ and }\frac{-\sqrt{2y\sqrt{4-y^{2}}+4}+\sqrt{-2y\sqrt{4-y^{2}}+4}}{2}\leq 0\text{ and }y\leq \sqrt{2}\text{ and }y\sqrt{4-y^{2}}\leq 2\right)\text{ or }|y|=\sqrt{2}\\x=-\frac{y\sqrt{4-y^{2}}}{2}\text{, }&\left(y\leq 0\text{ and }\frac{\sqrt{2y\sqrt{4-y^{2}}+4}-\sqrt{-2y\sqrt{4-y^{2}}+4}}{2}\geq 0\text{ and }y\geq -\sqrt{2}\text{ and }-y\sqrt{4-y^{2}}\leq 2\right)\text{ or }\left(y\geq 0\text{ and }\frac{\sqrt{2y\sqrt{4-y^{2}}+4}-\sqrt{-2y\sqrt{4-y^{2}}+4}}{2}\leq 0\text{ and }y\leq \sqrt{2}\text{ and }y\sqrt{4-y^{2}}\leq 2\right)\end{matrix}\right,$$

Ratkaise muuttujan y suhteen

$$y=\sqrt{x+1}-\sqrt{1-x}$$

$$|x|\leq 1$$