Whakaoti i te t^3-7t+6=0

$$t ^ { 3 } - 7 t + 6 = 0$$

Whakaoti mō t

$$t=1$$

$$t=-3$$

$$t=2$$

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

$$±6,±3,±2,±1$$

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.

$$t=1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te t-k o te pūrau mō ia pūtake k. Whakawehea te t^{3}-7t+6 ki te t-1, kia riro ko t^{2}+t-6. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$t^{2}+t-6=0$$

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 -6 mō te c i te ture pūrua.

$$t=\frac{-1±\sqrt{1^{2}-4\times 1\left(-6\right)}}{2}$$

Mahia ngā tātaitai.

$$t=\frac{-1±5}{2}$$

Whakaotia te whārite t^{2}+t-6=0 ina he tōrunga te ±, ina he tōraro te ±.

$$t=-3 t=2$$

Rārangitia ngā otinga katoa i kitea.

$$t=1 t=-3 t=2$$