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

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

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{-\sqrt{2}y^{2}+y^{2}+\sqrt{2}}-1}{1-y^{2}}\text{; }x=-\frac{\sqrt{-\sqrt{2}y^{2}+y^{2}+\sqrt{2}}+1}{1-y^{2}}\text{, }&y\neq 1\text{ and }y\neq -1\\x=\frac{\sqrt{2}-1}{2}\approx 0,207106781\text{, }&y=1\text{ or }y=-1\end{matrix}\right,$$

y uchun yechish (complex solution)

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

$$y=\frac{\sqrt{x^{2}+2x+1-\sqrt{2}}}{x}\text{, }x\neq 0$$

x uchun yechish

$$\left\{\begin{matrix}x=\frac{\sqrt{-\sqrt{2}y^{2}+y^{2}+\sqrt{2}}-1}{1-y^{2}}\text{; }x=-\frac{\sqrt{-\sqrt{2}y^{2}+y^{2}+\sqrt{2}}+1}{1-y^{2}}\text{, }&|y|\neq 1\text{ and }|y|\leq \sqrt[4]{2}\sqrt{\sqrt{2}+1}\\x=\frac{\sqrt{2}-1}{2}\text{, }&|y|=1\end{matrix}\right,$$

y uchun yechish

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

$$y=\frac{\sqrt{x^{2}+2x+1-\sqrt{2}}}{x}\text{, }x\geq \sqrt[4]{2}-1\text{ or }x\leq -\sqrt[4]{2}-1$$