Whakaoti i te n^3=-216

$$n ^ { 3 } = - 216$$

Whakaoti mō n (complex solution)

$$n=-3\sqrt{3}i+3\approx 3-5.196152423i$$

$$n=-6$$

$$n=3+3\sqrt{3}i\approx 3+5.196152423i$$

Ngā Upane Otinga

Me tāpiri te 216 ki ngā taha e rua.

$$n^{3}+216=0$$

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 216, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±216,±108,±72,±54,±36,±27,±24,±18,±12,±9,±8,±6,±4,±3,±2,±1$$

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.

$$n=-6$$

Mā te whakatakotoranga Tauwehe, he tauwehe te n-k o te pūrau mō ia pūtake k. Whakawehea te n^{3}+216 ki te n+6, kia riro ko n^{2}-6n+36. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$n^{2}-6n+36=0$$

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 -6 mō te b, me te 36 mō te c i te ture pūrua.

$$n=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 1\times 36}}{2}$$

Mahia ngā tātaitai.

$$n=\frac{6±\sqrt{-108}}{2}$$

Whakaotia te whārite n^{2}-6n+36=0 ina he tōrunga te ±, ina he tōraro te ±.

$$n=-3i\sqrt{3}+3 n=3+3i\sqrt{3}$$

Rārangitia ngā otinga katoa i kitea.

$$n=-6 n=-3i\sqrt{3}+3 n=3+3i\sqrt{3}$$

Whakaoti mō n

$$n=-6$$

Ngā Upane Otinga

Me tāpiri te 216 ki ngā taha e rua.

$$n^{3}+216=0$$

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 216, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±216,±108,±72,±54,±36,±27,±24,±18,±12,±9,±8,±6,±4,±3,±2,±1$$

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.

$$n=-6$$

Mā te whakatakotoranga Tauwehe, he tauwehe te n-k o te pūrau mō ia pūtake k. Whakawehea te n^{3}+216 ki te n+6, kia riro ko n^{2}-6n+36. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$n^{2}-6n+36=0$$

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 -6 mō te b, me te 36 mō te c i te ture pūrua.

$$n=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 1\times 36}}{2}$$

Mahia ngā tātaitai.

$$n=\frac{6±\sqrt{-108}}{2}$$

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

$$n\in \emptyset$$

Rārangitia ngā otinga katoa i kitea.

$$n=-6$$