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

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

x uchun yechish

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

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

Ildizli tenglamalarni yechish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

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

\frac{1}{3}e ni ikki tarafga qo’shing.

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

Ikki tarafini \frac{2}{3}e ga bo‘ling.

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

\frac{2}{3}e ga bo'lish \frac{2}{3}e ga ko'paytirishni bekor qiladi.

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

y+\frac{e}{3} ni \frac{2}{3}e ga bo'lish.

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

Tenglamaning ikkala taraf kvadratini chiqarish.

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

2 ni tenglamaning ikkala tarafiga qo'shish.

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

O‘zidan -2 ayirilsa 0 qoladi.

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

\frac{\left(e+3y\right)^{2}}{4e^{2}} dan -2 ni ayirish.

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

Ikki tarafini 2 ga bo‘ling.

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

2 ga bo'lish 2 ga ko'paytirishni bekor qiladi.

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

\frac{9}{4}+\frac{\frac{9y^{2}}{4}+\frac{3ye}{2}}{e^{2}} ni 2 ga bo'lish.

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

x uchun yechish (complex solution)

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

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

y uchun yechish (complex solution)

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

y uchun yechish

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

$$x\geq 1$$