Whakaoti i te 2x^3=16

$$2 x ^ { 3 } = 16$$

Whakaoti mō x (complex solution)

$$x=-\sqrt{3}i-1\approx -1-1.732050808i$$

$$x=2$$

$$x=-1+\sqrt{3}i\approx -1+1.732050808i$$

Ngā Upane Otinga

Whakawehea ngā taha e rua ki te 2.

$$x^{3}=\frac{16}{2}$$

Whakawehea te 16 ki te 2, kia riro ko 8.

$$x^{3}=8$$

Tangohia te 8 mai i ngā taha e rua.

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

Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau -8, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±8,±4,±2,±1$$

Kimihia tētahi pūtake pērā mā te whakamātau i ngā uara tau tōpū katoa, e tīmata ana i te mea iti rawa mā te uara pū. Mēnā kāore he pūtake tau tōpū e kitea, whakamātauria ngā hautanga.

$$x=2$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}-8 ki te x-2, kia riro ko x^{2}+2x+4. Whakaotihia te whārite ina ōrite te hua ki te 0.

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

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 2 mō te b, me te 4 mō te c i te ture pūrua.

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

Mahia ngā tātaitai.

$$x=\frac{-2±\sqrt{-12}}{2}$$

Whakaotia te whārite x^{2}+2x+4=0 ina he tōrunga te ±, ina he tōraro te ±.

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

Rārangitia ngā otinga katoa i kitea.

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

Whakaoti mō x

$$x=2$$

Ngā Upane Otinga

Whakawehea ngā taha e rua ki te 2.

$$x^{3}=\frac{16}{2}$$

Whakawehea te 16 ki te 2, kia riro ko 8.

$$x^{3}=8$$

Tangohia te 8 mai i ngā taha e rua.

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

Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau -8, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±8,±4,±2,±1$$

Kimihia tētahi pūtake pērā mā te whakamātau i ngā uara tau tōpū katoa, e tīmata ana i te mea iti rawa mā te uara pū. Mēnā kāore he pūtake tau tōpū e kitea, whakamātauria ngā hautanga.

$$x=2$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}-8 ki te x-2, kia riro ko x^{2}+2x+4. Whakaotihia te whārite ina ōrite te hua ki te 0.

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

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 2 mō te b, me te 4 mō te c i te ture pūrua.

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

Mahia ngā tātaitai.

$$x=\frac{-2±\sqrt{-12}}{2}$$

Tā te mea e kore te pūrua o tētahi tau tōraro e tautohutia ki te āpure tūturu, kāhore he rongoā.

$$x\in \emptyset$$

Rārangitia ngā otinga katoa i kitea.

$$x=2$$