Whakaoti i te x^2+3=0

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

Whakaoti mō x (complex solution)

$$x=-\sqrt{3}i\approx -0-1.732050808i$$

$$x=\sqrt{3}i\approx 1.732050808i$$

Ngā Upane mā te Kimi Pūtakerua

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

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

Kua oti te whārite te whakatau.

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

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.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, 0 mō b, me 3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua 0.

$$x=\frac{0±\sqrt{-4\times 3}}{2}$$

Whakareatia -4 ki te 3.

$$x=\frac{0±\sqrt{-12}}{2}$$

Tuhia te pūtakerua o te -12.

$$x=\frac{0±2\sqrt{3}i}{2}$$

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{3}i}{2} ina he tāpiri te ±.

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

Nā, me whakaoti te whārite x=\frac{0±2\sqrt{3}i}{2} ina he tango te ±.

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

Kua oti te whārite te whakatau.

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