Whakaoti i te 1/x=4x

$$\frac { 1 } { x } = 4 x$$

Whakaoti mō x

$$x=\frac{1}{2}=0.5$$

$$x=-\frac{1}{2}=-0.5$$

Ngā Upane mā te Kimi Pūtakerua

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

$$1=4xx$$

Whakareatia te x ki te x, ka x^{2}.

$$1=4x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$4x^{2}=1$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=\frac{1}{4}$$

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

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$1=4xx$$

Whakareatia te x ki te x, ka x^{2}.

$$1=4x^{2}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$4x^{2}=1$$

Tangohia te 1 mai i ngā taha e rua.

$$4x^{2}-1=0$$

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

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

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-1\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16\left(-1\right)}}{2\times 4}$$

Whakareatia -16 ki te -1.

$$x=\frac{0±\sqrt{16}}{2\times 4}$$

Tuhia te pūtakerua o te 16.

$$x=\frac{0±4}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±4}{8}$$

Nā, me whakaoti te whārite x=\frac{0±4}{8} ina he tāpiri te ±. Whakahekea te hautanga \frac{4}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$x=\frac{1}{2}$$

Nā, me whakaoti te whārite x=\frac{0±4}{8} ina he tango te ±. Whakahekea te hautanga \frac{-4}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Kua oti te whārite te whakatau.

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