Whakaoti i te 6x^2+5=3

$$6 x ^ { 2 } + 5 = 3$$

Whakaoti mō x (complex solution)

$$x=-\frac{\sqrt{3}i}{3}\approx -0-0.577350269i$$

$$x=\frac{\sqrt{3}i}{3}\approx 0.577350269i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 5 mai i ngā taha e rua.

$$6x^{2}=3-5$$

Tangohia te 5 i te 3, ka -2.

$$6x^{2}=-2$$

Whakawehea ngā taha e rua ki te 6.

$$x^{2}=\frac{-2}{6}$$

Whakahekea te hautanga \frac{-2}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x^{2}=-\frac{1}{3}$$

Kua oti te whārite te whakatau.

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 3 mai i ngā taha e rua.

$$6x^{2}+5-3=0$$

Tangohia te 3 i te 5, ka 2.

$$6x^{2}+2=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 6 mō a, 0 mō b, me 2 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\times 2}}{2\times 6}$$

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 6\times 2}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{0±\sqrt{-24\times 2}}{2\times 6}$$

Whakareatia -24 ki te 2.

$$x=\frac{0±\sqrt{-48}}{2\times 6}$$

Tuhia te pūtakerua o te -48.

$$x=\frac{0±4\sqrt{3}i}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{0±4\sqrt{3}i}{12}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{3}i}{12} ina he tāpiri te ±.

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

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{3}i}{12} ina he tango te ±.

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

Kua oti te whārite te whakatau.

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