Whakaoti i te x^2-2yx-y+1=0

$${ x }^{ 2 } -2yx-y+1=0$$

Whakaoti mō y

$$y=\frac{x^{2}+1}{2x+1}$$

$$x\neq -\frac{1}{2}$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te x^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-2yx-y+1=-x^{2}$$

Tangohia te 1 mai i ngā taha e rua.

$$-2yx-y=-x^{2}-1$$

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

$$\left(-2x-1\right)y=-x^{2}-1$$

Whakawehea ngā taha e rua ki te -2x-1.

$$\frac{\left(-2x-1\right)y}{-2x-1}=\frac{-x^{2}-1}{-2x-1}$$

Mā te whakawehe ki te -2x-1 ka wetekia te whakareanga ki te -2x-1.

$$y=\frac{-x^{2}-1}{-2x-1}$$

Whakawehe -x^{2}-1 ki te -2x-1.

$$y=\frac{x^{2}+1}{2x+1}$$

Whakaoti mō x (complex solution)

$$x=\sqrt{y^{2}+y-1}+y$$

$$x=-\sqrt{y^{2}+y-1}+y$$

Whakaoti mō x

$$x=\sqrt{y^{2}+y-1}+y$$

$$x=-\sqrt{y^{2}+y-1}+y\text{, }y\geq \frac{\sqrt{5}-1}{2}\text{ or }y\leq \frac{-\sqrt{5}-1}{2}$$