Whakaoti i te x^2=2y/y

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

Whakaoti mō x (complex solution)

$$x=-\sqrt{2}\approx -1.414213562$$

$$x=\sqrt{2}\approx 1.414213562\text{, }y\neq 0$$

Ngā Upane mā te Kimi Pūtakerua

Kua oti te whārite te whakatau.

$$x=\sqrt{2} x=-\sqrt{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$x^{2}=2$$

Me tango 2 mai i ngā taha e rua o te whārite.

$$x^{2}-2=2-2$$

Mā te tango i te 2 i a ia ake anō ka toe ko te 0.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me -2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua 0.

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

Whakareatia -4 ki te -2.

$$x=\frac{0±\sqrt{8}}{2}$$

Tuhia te pūtakerua o te 8.

$$x=\frac{0±2\sqrt{2}}{2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{2}}{2} ina he tāpiri te ±.

$$x=\sqrt{2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{2}}{2} ina he tango te ±.

$$x=-\sqrt{2}$$

Kua oti te whārite te whakatau.

$$x=\sqrt{2} x=-\sqrt{2}$$

Whakaoti mō y (complex solution)

$$y\neq 0$$

$$\left(x=-\sqrt{2}\text{ or }x=\sqrt{2}\right)\text{ and }y\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe y ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te y.

$$yx^{2}=2y$$

Tangohia te 2y mai i ngā taha e rua.

$$yx^{2}-2y=0$$

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

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

Whakawehe 0 ki te x^{2}-2.

$$y=0$$

Tē taea kia ōrite te tāupe y ki 0.

$$y\in \emptyset$$

Whakaoti mō y

$$y\neq 0$$

$$|x|=\sqrt{2}\text{ and }y\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe y ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te y.

$$yx^{2}=2y$$

Tangohia te 2y mai i ngā taha e rua.

$$yx^{2}-2y=0$$

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

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

Whakawehe 0 ki te x^{2}-2.

$$y=0$$

Tē taea kia ōrite te tāupe y ki 0.

$$y\in \emptyset$$

Whakaoti mō x

$$x=\sqrt{2}$$

$$x=-\sqrt{2}\text{, }y\neq 0$$