Réitigh y=2/3esqrt{2x-2}-1/3e

$$y = \frac { 2 } { 3 } e \sqrt { 2 x - 2 } - \frac { 1 } { 3 } e$$

Réitigh do x.

$$x=\frac{9\times \left(\frac{y}{e}\right)^{2}}{8}+\frac{3y}{4e}+\frac{9}{8}$$

$$y\geq -\frac{e}{3}$$

Céimeanna chun cothromóidí fréimhe a réiteach

Athraigh na taobhanna ionas go mbeidh na téarmaí inathraitheacha ar fad ar an taobh clé.

$$\frac{2}{3}e\sqrt{2x-2}-\frac{1}{3}e=y$$

Cuir \frac{1}{3}e leis an dá thaobh.

$$\frac{2}{3}e\sqrt{2x-2}=y+\frac{1}{3}e$$

Roinn an dá thaobh faoi \frac{2}{3}e.

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

Má roinntear é faoi \frac{2}{3}e cuirtear an iolrúchán faoi \frac{2}{3}e ar ceal.

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

Roinn y+\frac{e}{3} faoi \frac{2}{3}e.

$$\sqrt{2x-2}=\frac{3y}{2e}+\frac{1}{2}$$

Cearnaigh an dá thaobh den chothromóid.

$$2x-2=\frac{\left(3y+e\right)^{2}}{4e^{2}}$$

Cuir 2 leis an dá thaobh den chothromóid.

$$2x-2-\left(-2\right)=\frac{\left(3y+e\right)^{2}}{4e^{2}}-\left(-2\right)$$

Má dhealaítear -2 uaidh féin faightear 0.

$$2x=\frac{\left(3y+e\right)^{2}}{4e^{2}}-\left(-2\right)$$

Dealaigh -2 ó \frac{\left(e+3y\right)^{2}}{4e^{2}}.

$$2x=\frac{\frac{9y^{2}}{4}+\frac{3ey}{2}}{e^{2}}+\frac{9}{4}$$

Roinn an dá thaobh faoi 2.

$$\frac{2x}{2}=\frac{\frac{\frac{9y^{2}}{4}+\frac{3ey}{2}}{e^{2}}+\frac{9}{4}}{2}$$

Má roinntear é faoi 2 cuirtear an iolrúchán faoi 2 ar ceal.

$$x=\frac{\frac{\frac{9y^{2}}{4}+\frac{3ey}{2}}{e^{2}}+\frac{9}{4}}{2}$$

Roinn \frac{9}{4}+\frac{\frac{9y^{2}}{4}+\frac{3ye}{2}}{e^{2}} faoi 2.

$$x=\frac{\frac{9y^{2}}{8}+\frac{3ey}{4}}{e^{2}}+\frac{9}{8}$$

Réitigh do x. (complex solution)

$$x=\frac{9\times \left(\frac{y}{e}\right)^{2}}{8}+\frac{3y}{4e}+\frac{9}{8}$$

$$arg(3y+e)<\pi \text{ or }y=-\frac{e}{3}$$

Réitigh do y. (complex solution)

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

Réitigh do y.

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

$$x\geq 1$$