Réitigh (x^2-3)sqrt{2x+y}=0

$$( { x }^{ 2 } -3) \sqrt{ 2x+y } =0$$

Réitigh do y.

$$\left\{\begin{matrix}\\y=-2x\text{, }&\text{unconditionally}\\y\geq -2x\text{, }&|x|=\sqrt{3}\end{matrix}\right.$$

Céimeanna chun cothromóidí fréimhe a réiteach

Roinn an dá thaobh faoi x^{2}-3.

$$\frac{\left(x^{2}-3\right)\sqrt{y+2x}}{x^{2}-3}=\frac{0}{x^{2}-3}$$

Má roinntear é faoi x^{2}-3 cuirtear an iolrúchán faoi x^{2}-3 ar ceal.

$$\sqrt{y+2x}=\frac{0}{x^{2}-3}$$

Roinn 0 faoi x^{2}-3.

$$\sqrt{y+2x}=0$$

Cearnaigh an dá thaobh den chothromóid.

$$y+2x=0$$

Bain 2x ón dá thaobh den chothromóid.

$$y+2x-2x=-2x$$

Má dhealaítear 2x uaidh féin faightear 0.

$$y=-2x$$

Réitigh do x. (complex solution)

$$x=-\sqrt{3}\approx -1.732050808$$

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\frac{y}{2}$$

Réitigh do y. (complex solution)

$$\left\{\begin{matrix}\\y=-2x\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=-\sqrt{3}\text{ or }x=\sqrt{3}\end{matrix}\right.$$

Réitigh do x.

$$\left\{\begin{matrix}\\x=-\frac{y}{2}\text{, }&\text{unconditionally}\\x=-\sqrt{3}\text{, }&y\geq 2\sqrt{3}\\x=\sqrt{3}\approx 1.732050808\text{, }&y\geq -2\sqrt{3}\end{matrix}\right.$$