y=sqrt{xy} eching

$$y= \sqrt{ xy }$$

x uchun yechish

$$\left\{\begin{matrix}x=y\text{, }&y\geq 0\\x\in \mathrm{R}\text{, }&y=0\end{matrix}\right,$$

Ildizli tenglamalarni yechish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\sqrt{xy}=y$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$yx=y^{2}$$

Ikki tarafini y ga bo‘ling.

$$\frac{yx}{y}=\frac{y^{2}}{y}$$

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

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

y^{2} ni y ga bo'lish.

$$x=y$$

x uchun yechish (complex solution)

$$\left\{\begin{matrix}x=y\text{, }&arg(y)<\pi \text{ or }y=0\\x\in \mathrm{C}\text{, }&y=0\end{matrix}\right,$$

y uchun yechish (complex solution)

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=x\text{, }&arg(x)<\pi \text{ or }x=0\end{matrix}\right,$$

y uchun yechish

$$\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=x\text{, }&x\geq 0\end{matrix}\right,$$