Resolver sqrt{x+1}=sqrt[3]{y/2}-4/2

$$\sqrt { x + 1 } = \sqrt[ 3 ] { \frac { y } { 2 } } - \frac { 4 } { 2 }$$

Ebatzi: x

$$x=\frac{\sqrt[3]{2}y^{\frac{2}{3}}-4\times 2^{\frac{2}{3}}\sqrt[3]{y}+6}{2}$$

$$\frac{2^{\frac{2}{3}}\sqrt[3]{y}}{2}-2\geq 0$$

Ekuazio irrazionalak ebazteko urratsak

Egin ekuazioaren bi aldeak ber bi.

$$x+1=\frac{\left(\sqrt[3]{y}-2\sqrt[3]{2}\right)^{2}}{2^{\frac{2}{3}}}$$

Egin ken 1 ekuazioaren bi aldeetan.

$$x+1-1=\frac{\left(\sqrt[3]{y}-2\sqrt[3]{2}\right)^{2}}{2^{\frac{2}{3}}}-1$$

1 balioari bere burua kenduz gero, 0 da emaitza.

$$x=\frac{\left(\sqrt[3]{y}-2\sqrt[3]{2}\right)^{2}}{2^{\frac{2}{3}}}-1$$

Egin 1 ken \frac{\left(\sqrt[3]{y}-2\sqrt[3]{2}\right)^{2}}{2^{\frac{2}{3}}}.

$$x=\frac{y^{\frac{2}{3}}}{2^{\frac{2}{3}}}-\frac{4\sqrt[3]{y}}{\sqrt[3]{2}}+3$$

Ebatzi: x (complex solution)

$$x=\frac{\sqrt[3]{2}y^{\frac{2}{3}}-4\times 2^{\frac{2}{3}}\sqrt[3]{y}+6}{2}$$

$$arg(-\frac{2^{\frac{2}{3}}\sqrt[3]{y}}{2}+2)\geq \pi \text{ or }y=16$$

Ebatzi: y (complex solution)

$$y=2\left(\sqrt{x+1}+2\right)^{3}$$

$$arg(\sqrt{x+1}+2)<\frac{2\pi }{3}$$

Ebatzi: y

$$y=2\left(\sqrt{x+1}+2\right)^{3}$$

$$x\geq -1$$