Whakaoti i te 4x^2+quad+3=0

$$4 x ^ { 2 } + \quad + 3 = 0$$

Whakaoti mō x (complex solution)

$$x=-\frac{\sqrt{3}i}{2}\approx -0-0.866025404i$$

$$x=\frac{\sqrt{3}i}{2}\approx 0.866025404i$$

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.

$$4x^{2}=-3$$

Whakawehea ngā taha e rua ki te 4.

$$x^{2}=-\frac{3}{4}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{3}i}{2} x=-\frac{\sqrt{3}i}{2}$$

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.

$$4x^{2}+3=0$$

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

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

Pūrua 0.

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

Whakareatia -4 ki te 4.

$$x=\frac{0±\sqrt{-16\times 3}}{2\times 4}$$

Whakareatia -16 ki te 3.

$$x=\frac{0±\sqrt{-48}}{2\times 4}$$

Tuhia te pūtakerua o te -48.

$$x=\frac{0±4\sqrt{3}i}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{0±4\sqrt{3}i}{8}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{3}i}{8} ina he tāpiri te ±.

$$x=\frac{\sqrt{3}i}{2}$$

Nā, me whakaoti te whārite x=\frac{0±4\sqrt{3}i}{8} ina he tango te ±.

$$x=-\frac{\sqrt{3}i}{2}$$

Kua oti te whārite te whakatau.

$$x=\frac{\sqrt{3}i}{2} x=-\frac{\sqrt{3}i}{2}$$