Whakaoti i te x^6+3x^3+2=0

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

Whakaoti mō x (complex solution)

$$x\in \frac{-\sqrt{3}i+1}{2},-1,\frac{1+\sqrt{3}i}{2},\sqrt[3]{2}e^{\frac{5\pi i}{3}},\sqrt[3]{2}e^{\frac{\pi i}{3}},-\sqrt[3]{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{3}.

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

Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te 1 mō te a, te 3 mō te b, me te 2 mō te c i te ture pūrua.

$$t=\frac{-3±\sqrt{3^{2}-4\times 1\times 2}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{-3±1}{2}$$

Whakaotia te whārite t=\frac{-3±1}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=-1 t=-2$$

Mai i te x=t^{3}, ka taea ngā otinga mā te whakaoti te whārite mō ia t.

$$x=-1 x=\frac{1+\sqrt{3}i}{2} x=\frac{-\sqrt{3}i+1}{2} x=-\sqrt[3]{2}ie^{\frac{\pi i}{6}} x=-\sqrt[3]{2} x=\sqrt[3]{2}e^{\frac{\pi i}{3}}$$

Whakaoti mō x

$$x=-\sqrt[3]{2}\approx -1.25992105$$

$$x=-1$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{3}.

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

Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te 1 mō te a, te 3 mō te b, me te 2 mō te c i te ture pūrua.

$$t=\frac{-3±\sqrt{3^{2}-4\times 1\times 2}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{-3±1}{2}$$

Whakaotia te whārite t=\frac{-3±1}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=-1 t=-2$$

I te mea ko x=t^{3}, ka riro ngā otinga mā te arotake i te x=\sqrt[3]{t} mō ia t.

$$x=-1 x=-\sqrt[3]{2}$$