Whakaoti i te w^3=-64

$$w ^ { 3 } = - 64$$

Whakaoti mō w (complex solution)

$$w=-2\sqrt{3}i+2\approx 2-3.464101615i$$

$$w=-4$$

$$w=2+2\sqrt{3}i\approx 2+3.464101615i$$

Ngā Upane Otinga

Me tāpiri te 64 ki ngā taha e rua.

$$w^{3}+64=0$$

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

$$±64,±32,±16,±8,±4,±2,±1$$

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.

$$w=-4$$

Mā te whakatakotoranga Tauwehe, he tauwehe te w-k o te pūrau mō ia pūtake k. Whakawehea te w^{3}+64 ki te w+4, kia riro ko w^{2}-4w+16. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$w^{2}-4w+16=0$$

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 -4 mō te b, me te 16 mō te c i te ture pūrua.

$$w=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 1\times 16}}{2}$$

Mahia ngā tātaitai.

$$w=\frac{4±\sqrt{-48}}{2}$$

Whakaotia te whārite w^{2}-4w+16=0 ina he tōrunga te ±, ina he tōraro te ±.

$$w=-2i\sqrt{3}+2 w=2+2i\sqrt{3}$$

Rārangitia ngā otinga katoa i kitea.

$$w=-4 w=-2i\sqrt{3}+2 w=2+2i\sqrt{3}$$

Whakaoti mō w

$$w=-4$$

Ngā Upane Otinga

Me tāpiri te 64 ki ngā taha e rua.

$$w^{3}+64=0$$

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

$$±64,±32,±16,±8,±4,±2,±1$$

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.

$$w=-4$$

Mā te whakatakotoranga Tauwehe, he tauwehe te w-k o te pūrau mō ia pūtake k. Whakawehea te w^{3}+64 ki te w+4, kia riro ko w^{2}-4w+16. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$w^{2}-4w+16=0$$

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 -4 mō te b, me te 16 mō te c i te ture pūrua.

$$w=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 1\times 16}}{2}$$

Mahia ngā tātaitai.

$$w=\frac{4±\sqrt{-48}}{2}$$

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

$$w\in \emptyset$$

Rārangitia ngā otinga katoa i kitea.

$$w=-4$$