Whakaoti i te t^3+t-2=0

$$t ^ { 3 } + t - 2 = 0$$

Whakaoti mō t (complex solution)

$$t=\frac{-\sqrt{7}i-1}{2}\approx -0.5-1.322875656i$$

$$t=1$$

$$t=\frac{-1+\sqrt{7}i}{2}\approx -0.5+1.322875656i$$

Ngā Upane Otinga

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 -2, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±2,±1$$

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.

$$t=1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te t-k o te pūrau mō ia pūtake k. Whakawehea te t^{3}+t-2 ki te t-1, kia riro ko t^{2}+t+2. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$t^{2}+t+2=0$$

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 2 mō te c i te ture pūrua.

$$t=\frac{-1±\sqrt{1^{2}-4\times 1\times 2}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{-1±\sqrt{-7}}{2}$$

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

$$t=\frac{-\sqrt{7}i-1}{2} t=\frac{-1+\sqrt{7}i}{2}$$

Rārangitia ngā otinga katoa i kitea.

$$t=1 t=\frac{-\sqrt{7}i-1}{2} t=\frac{-1+\sqrt{7}i}{2}$$

Whakaoti mō t

$$t=1$$

Ngā Upane Otinga

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 -2, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±2,±1$$

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.

$$t=1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te t-k o te pūrau mō ia pūtake k. Whakawehea te t^{3}+t-2 ki te t-1, kia riro ko t^{2}+t+2. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$t^{2}+t+2=0$$

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 2 mō te c i te ture pūrua.

$$t=\frac{-1±\sqrt{1^{2}-4\times 1\times 2}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{-1±\sqrt{-7}}{2}$$

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

$$t\in \emptyset$$

Rārangitia ngā otinga katoa i kitea.

$$t=1$$