Whakaoti i te a^3+5a^2-18a-72=0

$$a ^ { 3 } + 5 a ^ { 2 } - 18 a - 72 = 0$$

Whakaoti mō a

$$a=-3$$

$$a=4$$

$$a=-6$$

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 -72, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±72,±36,±24,±18,±12,±9,±8,±6,±4,±3,±2,±1$$

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.

$$a=-3$$

Mā te whakatakotoranga Tauwehe, he tauwehe te a-k o te pūrau mō ia pūtake k. Whakawehea te a^{3}+5a^{2}-18a-72 ki te a+3, kia riro ko a^{2}+2a-24. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$a^{2}+2a-24=0$$

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 2 mō te b, me te -24 mō te c i te ture pūrua.

$$a=\frac{-2±\sqrt{2^{2}-4\times 1\left(-24\right)}}{2}$$

Mahia ngā tātaitai.

$$a=\frac{-2±10}{2}$$

Whakaotia te whārite a^{2}+2a-24=0 ina he tōrunga te ±, ina he tōraro te ±.

$$a=-6 a=4$$

Rārangitia ngā otinga katoa i kitea.

$$a=-3 a=-6 a=4$$