Løs y^2=x+y^4

$${ y }^{ 2 } = x+ { y }^{ 4 }$$

Løs for x

$$x=y^{2}-y^{4}$$

Løsningsvejledning

Skift side, så alle variable led er placeret på venstre side.

$$x+y^{4}=y^{2}$$

Subtraher y^{4} fra begge sider.

$$x=y^{2}-y^{4}$$

Løs for y (complex solution)

$$y=\frac{\sqrt{2\sqrt{1-4x}+2}}{2}$$

$$y=-\frac{\sqrt{2\sqrt{1-4x}+2}}{2}$$

$$y=-\frac{\sqrt{-2\sqrt{1-4x}+2}}{2}$$

$$y=\frac{\sqrt{-2\sqrt{1-4x}+2}}{2}$$

Løs for y

$$\left\{\begin{matrix}y=-\frac{\sqrt{-2\sqrt{1-4x}+2}}{2}\text{; }y=\frac{\sqrt{-2\sqrt{1-4x}+2}}{2}\text{, }&x\geq 0\text{ and }x\leq \frac{1}{4}\\y=-\frac{\sqrt{2\sqrt{1-4x}+2}}{2}\text{; }y=\frac{\sqrt{2\sqrt{1-4x}+2}}{2}\text{, }&x\leq \frac{1}{4}\end{matrix}\right,$$