Whakaoti i te 5p^3+5p^2-7p=7

$$5 p ^ { 3 } + 5 p ^ { 2 } - 7 p = 7$$

Whakaoti mō p

$$p = \frac{\sqrt{35}}{5} \approx 1.183215957$$

$$p = -\frac{\sqrt{35}}{5} \approx -1.183215957$$

$$p=-1$$

Ngā Upane Otinga

Tangohia te 7 mai i ngā taha e rua.

$$5p^{3}+5p^{2}-7p-7=0$$

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 -7, ā, ka wehea e q te whakarea arahanga 5. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±\frac{7}{5},±7,±\frac{1}{5},±1$$

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.

$$p=-1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te p-k o te pūrau mō ia pūtake k. Whakawehea te 5p^{3}+5p^{2}-7p-7 ki te p+1, kia riro ko 5p^{2}-7. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$5p^{2}-7=0$$

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 5 mō te a, te 0 mō te b, me te -7 mō te c i te ture pūrua.

$$p=\frac{0±\sqrt{0^{2}-4\times 5\left(-7\right)}}{2\times 5}$$

Mahia ngā tātaitai.

$$p=\frac{0±2\sqrt{35}}{10}$$

Whakaotia te whārite 5p^{2}-7=0 ina he tōrunga te ±, ina he tōraro te ±.

$$p=-\frac{\sqrt{35}}{5} p=\frac{\sqrt{35}}{5}$$

Rārangitia ngā otinga katoa i kitea.

$$p=-1 p=-\frac{\sqrt{35}}{5} p=\frac{\sqrt{35}}{5}$$