Whakaoti i te lambda^3-27lambda^2+243lambda-729=0

$$\lambda ^ { 3 } - 27 \lambda ^ { 2 } + 243 \lambda - 729 = 0$$

Whakaoti mō λ

$$\lambda =9$$

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 -729, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±729,±243,±81,±27,±9,±3,±1$$

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.

$$\lambda =9$$

Mā te whakatakotoranga Tauwehe, he tauwehe te \lambda -k o te pūrau mō ia pūtake k. Whakawehea te \lambda ^{3}-27\lambda ^{2}+243\lambda -729 ki te \lambda -9, kia riro ko \lambda ^{2}-18\lambda +81. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$\lambda ^{2}-18\lambda +81=0$$

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 -18 mō te b, me te 81 mō te c i te ture pūrua.

$$\lambda =\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 1\times 81}}{2}$$

Mahia ngā tātaitai.

$$\lambda =\frac{18±0}{2}$$

He ōrite ngā whakatau.

$$\lambda =9$$