Tīpoka ki ngā ihirangi matua
Whakaoti mō x (complex solution)
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Whakaoti mō x
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Ngā Raru Ōrite mai i te Rapu Tukutuku

Tohaina

x^{3}-8=0
Tangohia te 8 mai i ngā taha e rua.
±8,±4,±2,±1
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}.
x=2
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}+2x+4=0
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=\frac{-2±\sqrt{2^{2}-4\times 1\times 4}}{2}
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{-12}}{2}
Mahia ngā tātaitai.
x=-\sqrt{3}i-1 x=-1+\sqrt{3}i
Whakaotia te whārite x^{2}+2x+4=0 ina he tōrunga te ±, ina he tōraro te ±.
x=2 x=-\sqrt{3}i-1 x=-1+\sqrt{3}i
Rārangitia ngā otinga katoa i kitea.
x^{3}-8=0
Tangohia te 8 mai i ngā taha e rua.
±8,±4,±2,±1
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}.
x=2
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}+2x+4=0
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=\frac{-2±\sqrt{2^{2}-4\times 1\times 4}}{2}
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{-12}}{2}
Mahia ngā tātaitai.
x\in \emptyset
Tā te mea e kore te pūrua o tētahi tau tōraro e tautohutia ki te āpure tūturu, kāhore he rongoā.
x=2
Rārangitia ngā otinga katoa i kitea.