Atrisiniet ysqrt{x}-1=y-sqrt{x}

$$y \sqrt{ x } -1=y- \sqrt{ x }$$

Atrast y (complex solution)

$$\left\{\begin{matrix}y=-1\text{, }&x\neq 1\\y\in \mathrm{C}\text{, }&x=1\end{matrix}\right,$$

Lineāra vienādojuma risināšanas darbības

Atņemiet y no abām pusēm.

$$y\sqrt{x}-1-y=-\sqrt{x}$$

Pievienot 1 abās pusēs.

$$y\sqrt{x}-y=-\sqrt{x}+1$$

Savelciet visus locekļus, kuros ir y.

$$\left(\sqrt{x}-1\right)y=-\sqrt{x}+1$$

Daliet abas puses ar \sqrt{x}-1.

$$\frac{\left(\sqrt{x}-1\right)y}{\sqrt{x}-1}=\frac{-\sqrt{x}+1}{\sqrt{x}-1}$$

Dalīšana ar \sqrt{x}-1 atsauc reizināšanu ar \sqrt{x}-1.

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

Daliet -\sqrt{x}+1 ar \sqrt{x}-1.

$$y=-1$$

Atrast y

$$\left\{\begin{matrix}y=-1\text{, }&x\neq 1\text{ and }x\geq 0\\y\in \mathrm{R}\text{, }&x=1\end{matrix}\right,$$

Lineāra vienādojuma risināšanas darbības

Atņemiet y no abām pusēm.

$$y\sqrt{x}-1-y=-\sqrt{x}$$

Pievienot 1 abās pusēs.

$$y\sqrt{x}-y=-\sqrt{x}+1$$

Savelciet visus locekļus, kuros ir y.

$$\left(\sqrt{x}-1\right)y=-\sqrt{x}+1$$

Daliet abas puses ar \sqrt{x}-1.

$$\frac{\left(\sqrt{x}-1\right)y}{\sqrt{x}-1}=\frac{-\sqrt{x}+1}{\sqrt{x}-1}$$

Dalīšana ar \sqrt{x}-1 atsauc reizināšanu ar \sqrt{x}-1.

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

Daliet -\sqrt{x}+1 ar \sqrt{x}-1.

$$y=-1$$

Atrast x (complex solution)

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=-1\end{matrix}\right,$$

Atrast x

$$\left\{\begin{matrix}\\x=1\text{, }&\text{unconditionally}\\x\geq 0\text{, }&y=-1\end{matrix}\right,$$