Whakaoti i te (x+1)^3+27=0

$$( x + 1 ) ^ { 3 } + 27 = 0$$

Whakaoti mō x (complex solution)

$$x=-4$$

$$x=\frac{1+3\sqrt{3}i}{2}\approx 0.5+2.598076211i$$

$$x=\frac{-3\sqrt{3}i+1}{2}\approx 0.5-2.598076211i$$

Ngā Upane Otinga

Me whakaroha te kīanga.

$$x^{3}+3x^{2}+3x+28=0$$

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

$$±28,±14,±7,±4,±2,±1$$

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.

$$x=-4$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}+3x^{2}+3x+28 ki te x+4, kia riro ko x^{2}-x+7. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$x^{2}-x+7=0$$

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 -1 mō te b, me te 7 mō te c i te ture pūrua.

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

Mahia ngā tātaitai.

$$x=\frac{1±\sqrt{-27}}{2}$$

Whakaotia te whārite x^{2}-x+7=0 ina he tōrunga te ±, ina he tōraro te ±.

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

Rārangitia ngā otinga katoa i kitea.

$$x=-4 x=\frac{-3i\sqrt{3}+1}{2} x=\frac{1+3i\sqrt{3}}{2}$$

Whakaoti mō x

$$x=-4$$

Ngā Upane Otinga

Me whakaroha te kīanga.

$$x^{3}+3x^{2}+3x+28=0$$

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

$$±28,±14,±7,±4,±2,±1$$

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.

$$x=-4$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}+3x^{2}+3x+28 ki te x+4, kia riro ko x^{2}-x+7. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$x^{2}-x+7=0$$

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 -1 mō te b, me te 7 mō te c i te ture pūrua.

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

Mahia ngā tātaitai.

$$x=\frac{1±\sqrt{-27}}{2}$$

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.

$$x=-4$$