Whakaoti i te u^3=216,u

$$u ^ { 3 } = 216 , u$$

Whakaoti mō u

$$u=6$$

Ngā Upane Otinga

Tangohia te 216 mai i ngā taha e rua.

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

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.

$$u=6$$

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

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

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.

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

Mahia ngā tātaitai.

$$u=\frac{-6±\sqrt{-108}}{2}$$

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

$$u\in \emptyset$$

Rārangitia ngā otinga katoa i kitea.

$$u=6$$