Resolver y=sqrt{x+y}

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

Resolver x

$$x=y\left(y-1\right)$$

$$y\geq 0$$

Pasos para resolver ecuacións radicais

Cambia de lado para que todos os termos variables estean no lado esquerdo.

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

Eleva ao cadrado ambos lados da ecuación.

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

Resta y en ambos lados da ecuación.

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

Se restas y a si mesmo, quédache 0.

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

Resta y de y^{2}.

$$x=y\left(y-1\right)$$

Resolver x (complex solution)

$$x=y\left(y-1\right)$$

$$arg(y)<\pi \text{ or }y=0$$

Resolver y (complex solution)

$$\left\{\begin{matrix}y=\frac{-\sqrt{4x+1}+1}{2}\text{, }&arg(\frac{-\sqrt{4x+1}+1}{2})<\pi \text{ or }x=0\\y=\frac{\sqrt{4x+1}+1}{2}\text{, }&arg(\frac{\sqrt{4x+1}+1}{2})<\pi \end{matrix}\right.$$

Resolver y

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