Whakaoti i te m^3-4m^2+5m-2=0

$${ m }^{ 3 } -4 { m }^{ 2 } +5m-2 = 0$$

Whakaoti mō m

$$m=1$$

$$m=2$$

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 -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.

$$m=1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te m-k o te pūrau mō ia pūtake k. Whakawehea te m^{3}-4m^{2}+5m-2 ki te m-1, kia riro ko m^{2}-3m+2. Whakaotihia te whārite ina ōrite te hua ki te 0.

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

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 -3 mō te b, me te 2 mō te c i te ture pūrua.

$$m=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 1\times 2}}{2}$$

Mahia ngā tātaitai.

$$m=\frac{3±1}{2}$$

Whakaotia te whārite m^{2}-3m+2=0 ina he tōrunga te ±, ina he tōraro te ±.

$$m=1 m=2$$

Rārangitia ngā otinga katoa i kitea.

$$m=1 m=2$$