Whakaoti i te (x^3-1):5=43

$$( x ^ { 3 } - 1 ) : 5 = 43$$

Whakaoti mō x (complex solution)

$$x=-3\sqrt{3}i-3\approx -3-5.196152423i$$

$$x=6$$

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

Ngā Upane Otinga

Me whakarea ngā taha e rua ki te 5.

$$x^{3}-1=43\times 5$$

Whakareatia te 43 ki te 5, ka 215.

$$x^{3}-1=215$$

Tangohia te 215 mai i ngā taha e rua.

$$x^{3}-1-215=0$$

Tangohia te 215 i te -1, ka -216.

$$x^{3}-216=0$$

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.

$$x=6$$

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

$$x^{2}+6x+36=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 1\times 36}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{-6±\sqrt{-108}}{2}$$

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

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

Rārangitia ngā otinga katoa i kitea.

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

Whakaoti mō x

$$x=6$$

Ngā Upane Otinga

Me whakarea ngā taha e rua ki te 5.

$$x^{3}-1=43\times 5$$

Whakareatia te 43 ki te 5, ka 215.

$$x^{3}-1=215$$

Tangohia te 215 mai i ngā taha e rua.

$$x^{3}-1-215=0$$

Tangohia te 215 i te -1, ka -216.

$$x^{3}-216=0$$

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.

$$x=6$$

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

$$x^{2}+6x+36=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 1\times 36}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{-6±\sqrt{-108}}{2}$$

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

$$x\in \emptyset$$

Rārangitia ngā otinga katoa i kitea.

$$x=6$$