Whakaoti i te ysqrt{x}-1=y-sqrt{x}

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

Whakaoti mō y (complex solution)

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te y mai i ngā taha e rua.

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

Me tāpiri te 1 ki ngā taha e rua.

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

Pahekotia ngā kīanga tau katoa e whai ana i te y.

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

Whakawehea ngā taha e rua ki te \sqrt{x}-1.

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

Mā te whakawehe ki te \sqrt{x}-1 ka wetekia te whakareanga ki te \sqrt{x}-1.

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

Whakawehe -\sqrt{x}+1 ki te \sqrt{x}-1.

$$y=-1$$

Whakaoti mō y

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te y mai i ngā taha e rua.

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

Me tāpiri te 1 ki ngā taha e rua.

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

Pahekotia ngā kīanga tau katoa e whai ana i te y.

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

Whakawehea ngā taha e rua ki te \sqrt{x}-1.

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

Mā te whakawehe ki te \sqrt{x}-1 ka wetekia te whakareanga ki te \sqrt{x}-1.

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

Whakawehe -\sqrt{x}+1 ki te \sqrt{x}-1.

$$y=-1$$

Whakaoti mō x (complex solution)

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

Whakaoti mō x

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