x=sqrt{xy} eching

$$x = \sqrt { x y }$$

y uchun yechish

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

Ildizli tenglamalarni yechish qadamlari

Tomonlarni almashtirib, barcha oʻzgaruvchi shartlar chap tomonga oʻtkazing.

$$\sqrt{xy}=x$$

Tenglamaning ikkala taraf kvadratini chiqarish.

$$xy=x^{2}$$

Ikki tarafini x ga bo‘ling.

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

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

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

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

$$y=x$$

x uchun yechish (complex solution)

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

y uchun yechish (complex solution)

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

x uchun yechish

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