解決y=x^2+y^2x/2 |Microsoft數學求解器

$$y = x ^ { 2 } + \frac { y ^ { 2 } x } { 2 }$$

解 x (復數求解)

$$x=\frac{-\sqrt{y^{4}+16y}-y^{2}}{4}$$

$$x=\frac{\sqrt{y^{4}+16y}-y^{2}}{4}$$

解 y (復數求解)

$$\left\{\begin{matrix}y=-\frac{\sqrt{1-2x^{3}}-1}{x}\text{; }y=\frac{\sqrt{1-2x^{3}}+1}{x}\text{, }&x\neq 0\\y=0\text{, }&x=0\end{matrix}\right.$$

解 x

$$x=\frac{-\sqrt{y^{4}+16y}-y^{2}}{4}$$

$$x=\frac{\sqrt{y^{4}+16y}-y^{2}}{4}\text{, }y\leq -2^{\frac{4}{3}}\text{ or }y\geq 0$$

解 y

$$\left\{\begin{matrix}y=-\frac{\sqrt{1-2x^{3}}-1}{x}\text{; }y=\frac{\sqrt{1-2x^{3}}+1}{x}\text{, }&x\neq 0\text{ and }x\leq \frac{2^{\frac{2}{3}}}{2}\\y=0\text{, }&x=0\end{matrix}\right.$$