Whakaoti i te 3x^2+5-2=0

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

Whakaoti mō x (complex solution)

$$x=-i$$

$$x=i$$

Ngā Upane mā te Kimi Pūtakerua

Tangohia te 2 i te 5, ka 3.

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

Tangohia te 3 mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

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

Whakawehea ngā taha e rua ki te 3.

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

Whakawehea te -3 ki te 3, kia riro ko -1.

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

Kua oti te whārite te whakatau.

$$x=i x=-i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 2 i te 5, ka 3.

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

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

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

Pūrua 0.

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

Whakareatia -4 ki te 3.

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

Whakareatia -12 ki te 3.

$$x=\frac{0±\sqrt{-36}}{2\times 3}$$

Tuhia te pūtakerua o te -36.

$$x=\frac{0±6i}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{0±6i}{6}$$

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

$$x=i$$

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

$$x=-i$$

Kua oti te whārite te whakatau.

$$x=i x=-i$$