Riješi x=sqrt{2+x+y}

$$x= \sqrt{ 2+x+y }$$

Izračunaj y

$$y=\left(x-2\right)\left(x+1\right)$$

$$x\geq 0$$

Koraci rješavanja iracionalnih jednadžbi

Zamijenite strane tako da svi izrazi s nepoznanicama budu s lijeve strane.

$$\sqrt{2+x+y}=x$$

Kvadrirajte obje strane jednadžbe.

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

Oduzmite 2+x od obiju strana jednadžbe.

$$y+x+2-\left(x+2\right)=x^{2}-\left(x+2\right)$$

Oduzimanje 2+x samog od sebe dobiva se 0.

$$y=x^{2}-\left(x+2\right)$$

Oduzmite 2+x od x^{2}.

$$y=\left(x-2\right)\left(x+1\right)$$

Izračunaj x (complex solution)

$$\left\{\begin{matrix}x=\frac{-\sqrt{4y+9}+1}{2}\text{, }&arg(\frac{-\sqrt{4y+9}+1}{2})<\pi \text{ or }y=-2\\x=\frac{\sqrt{4y+9}+1}{2}\text{, }&arg(\frac{\sqrt{4y+9}+1}{2})<\pi \end{matrix}\right,$$

Izračunaj y (complex solution)

$$y=\left(x-2\right)\left(x+1\right)$$

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

Izračunaj x

$$\left\{\begin{matrix}x=\frac{\sqrt{4y+9}+1}{2}\text{, }&y\geq -\frac{9}{4}\\x=\frac{-\sqrt{4y+9}+1}{2}\text{, }&y\geq -\frac{9}{4}\text{ and }y\leq -2\end{matrix}\right,$$