Whakaoti i te 3x^2+2=0

$$3 { x }^{ 2 } +2=0$$

Whakaoti mō x (complex solution)

$$x=-\frac{\sqrt{6}i}{3}\approx -0-0.816496581i$$

$$x=\frac{\sqrt{6}i}{3}\approx 0.816496581i$$

Ngā Upane mā te Kimi Pūtakerua

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

$$3x^{2}=-2$$

Whakawehea ngā taha e rua ki te 3.

$$x^{2}=-\frac{2}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{6}i}{3} x=-\frac{\sqrt{6}i}{3}$$

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.

$$3x^{2}+2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, 0 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\times 2}}{2\times 3}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3\times 2}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12\times 2}}{2\times 3}$$

Whakareatia -12 ki te 2.

$$x=\frac{0±\sqrt{-24}}{2\times 3}$$

Tuhia te pūtakerua o te -24.

$$x=\frac{0±2\sqrt{6}i}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±2\sqrt{6}i}{6}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{6}i}{6} ina he tāpiri te ±.

$$x=\frac{\sqrt{6}i}{3}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{6}i}{6} ina he tango te ±.

$$x=-\frac{\sqrt{6}i}{3}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{6}i}{3} x=-\frac{\sqrt{6}i}{3}$$