Whakaoti i te 2x-1/x=0

$$2 x - \frac { 1 } { x } = 0$$

Whakaoti mō x

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

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.

$$2xx-1=0$$

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

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

Me tāpiri te 1 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

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

Whakawehea ngā taha e rua ki te 2.

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

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

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

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.

$$2xx-1=0$$

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

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

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

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

Pūrua 0.

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

Whakareatia -4 ki te 2.

$$x=\frac{0±\sqrt{-8\left(-1\right)}}{2\times 2}$$

Whakareatia -8 ki te -1.

$$x=\frac{0±\sqrt{8}}{2\times 2}$$

Tuhia te pūtakerua o te 8.

$$x=\frac{0±2\sqrt{2}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{0±2\sqrt{2}}{4}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{2}}{4} ina he tāpiri te ±.

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

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{2}}{4} ina he tango te ±.

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

Kua oti te whārite te whakatau.

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