Whakaoti i te x^6-7x^3-8=0

$$x ^ { 6 } - 7 x ^ { 3 } - 8 = 0$$

Whakaoti mō x (complex solution)

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{3}.

$$t^{2}-7t-8=0$$

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 -7 mō te b, me te -8 mō te c i te ture pūrua.

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 1\left(-8\right)}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{7±9}{2}$$

Whakaotia te whārite t=\frac{7±9}{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.

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

Whakaoti mō x

$$x=-1$$

$$x=2$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakakapia te t mō te x^{3}.

$$t^{2}-7t-8=0$$

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 -7 mō te b, me te -8 mō te c i te ture pūrua.

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 1\left(-8\right)}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{7±9}{2}$$

Whakaotia te whārite t=\frac{7±9}{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.

$$x=2 x=-1$$