Whakaoti i te x^6-9x^3+8=0

$${ x }^{ 6 } -9 { x }^{ 3 } +8=0$$

Whakaoti mō x (complex solution)

$$x\in 2,-1+\sqrt{3}i,-\sqrt{3}i-1,\frac{-1+\sqrt{3}i}{2},1,\frac{-\sqrt{3}i-1}{2}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{3}.

$$t^{2}-9t+8=0$$

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 -9 mō te b, me te 8 mō te c i te ture pūrua.

$$t=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 1\times 8}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{9±7}{2}$$

Whakaotia te whārite t=\frac{9±7}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=8 t=1$$

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

$$x=-1+\sqrt{3}i x=-\sqrt{3}i-1 x=2 x=\frac{-1+\sqrt{3}i}{2} x=\frac{-\sqrt{3}i-1}{2} x=1$$

Whakaoti mō x

$$x=1$$

$$x=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{3}.

$$t^{2}-9t+8=0$$

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 -9 mō te b, me te 8 mō te c i te ture pūrua.

$$t=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 1\times 8}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{9±7}{2}$$

Whakaotia te whārite t=\frac{9±7}{2} ina he tōrunga te ±, ina he tōraro te ±.

$$t=8 t=1$$

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

$$x=2 x=1$$