Issolvi y=2/3esqrt{2x-2}-1/3e

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

Solvi għal x

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

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

Passi biex Issolvi l-Ekwazzjonijiet Radikali

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

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

Żid \frac{1}{3}e maż-żewġ naħat.

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

Iddividi ż-żewġ naħat b'\frac{2}{3}e.

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

Meta tiddividi b'\frac{2}{3}e titneħħa l-multiplikazzjoni b'\frac{2}{3}e.

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

Iddividi y+\frac{e}{3} b'\frac{2}{3}e.

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

Ikkwadra ż-żewġ naħat tal-ekwazzjoni.

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

Żid 2 maż-żewġ naħat tal-ekwazzjoni.

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

Jekk tnaqqas -2 minnu nnifsu jibqa' 0.

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

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

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

Iddividi ż-żewġ naħat b'2.

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

Meta tiddividi b'2 titneħħa l-multiplikazzjoni b'2.

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

Iddividi \frac{9}{4}+\frac{\frac{9y^{2}}{4}+\frac{3ye}{2}}{e^{2}} b'2.

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

Solvi għal x (complex solution)

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

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

Solvi għal y (complex solution)

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

Solvi għal y

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

$$x\geq 1$$