Whakaoti i te left(yxright)^2-4*x^2*1=0

$${ \left(yx \right) }^{ 2 } -4 \times { x }^{ 2 } \times 1=0$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{C}\text{, }&y=-2\text{ or }y=2\end{matrix}\right.$$

Ngā Upane mā te Kimi Pūtakerua

Whakarohaina te \left(yx\right)^{2}.

$$y^{2}x^{2}-4x^{2}\times 1=0$$

Whakareatia te 4 ki te 1, ka 4.

$$y^{2}x^{2}-4x^{2}=0$$

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

$$\left(y^{2}-4\right)x^{2}=0$$

Mā te whakawehe ki te y^{2}-4 ka wetekia te whakareanga ki te y^{2}-4.

$$x^{2}=\frac{0}{y^{2}-4}$$

Whakawehe 0 ki te y^{2}-4.

$$x^{2}=0$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$x=0 x=0$$

Kua oti te whārite te whakatau. He ōrite ngā whakatau.

$$x=0$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakarohaina te \left(yx\right)^{2}.

$$y^{2}x^{2}-4x^{2}\times 1=0$$

Whakareatia te 4 ki te 1, ka 4.

$$y^{2}x^{2}-4x^{2}=0$$

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

$$\left(y^{2}-4\right)x^{2}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi y^{2}-4 mō a, 0 mō b, me 0 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}}}{2\left(y^{2}-4\right)}$$

Tuhia te pūtakerua o te 0^{2}.

$$x=\frac{0±0}{2\left(y^{2}-4\right)}$$

Whakareatia 2 ki te y^{2}-4.

$$x=\frac{0}{2y^{2}-8}$$

Whakawehe 0 ki te 2y^{2}-8.

$$x=0$$

Whakaoti mō y (complex solution)

$$\left\{\begin{matrix}\\y=2\text{; }y=-2\text{, }&\text{unconditionally}\\y\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Whakaoti mō x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&|y|=2\end{matrix}\right.$$

Whakaoti mō y

$$\left\{\begin{matrix}y\in \mathrm{R}\text{, }&x=0\\y=2\text{; }y=-2\text{, }&x\neq 0\end{matrix}\right.$$