Whakaoti i te b^4-10b^2+9

$$b ^ { 4 } - 10 b ^ { 2 } + 9$$

Tauwehe

$$\left(b-3\right)\left(b-1\right)\left(b+1\right)\left(b+3\right)$$

Ngā Upane Otinga

Kia tauwehea ai te kīanga, me whakaoti te whārite ina ōrite ki te 0.

$$b^{4}-10b^{2}+9=0$$

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

$$±9,±3,±1$$

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.

$$b=1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te b-k o te pūrau mō ia pūtake k. Whakawehea te b^{4}-10b^{2}+9 ki te b-1, kia riro ko b^{3}+b^{2}-9b-9. Kia tauwehea ai te otinga, me whakaoti te whārite ina ōrite ki te 0.

$$b^{3}+b^{2}-9b-9=0$$

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 -9, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±9,±3,±1$$

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.

$$b=-1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te b-k o te pūrau mō ia pūtake k. Whakawehea te b^{3}+b^{2}-9b-9 ki te b+1, kia riro ko b^{2}-9. Kia tauwehea ai te otinga, me whakaoti te whārite ina ōrite ki te 0.

$$b^{2}-9=0$$

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 0 mō te b, me te -9 mō te c i te ture pūrua.

$$b=\frac{0±\sqrt{0^{2}-4\times 1\left(-9\right)}}{2}$$

Mahia ngā tātaitai.

$$b=\frac{0±6}{2}$$

Whakaotia te whārite b^{2}-9=0 ina he tōrunga te ±, ina he tōraro te ±.

$$b=-3 b=3$$

Me tuhi anō te kīanga whakatauwehe mā ngā pūtake i riro.

$$\left(b-3\right)\left(b-1\right)\left(b+1\right)\left(b+3\right)$$

Aromātai

$$b^{4}-10b^{2}+9$$