Whakaoti i te f(x)=x^3-7x^2-14x=6

$$f ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 14 x = 6$$

Whakaoti mō x

$$x=\sqrt{22}+4\approx 8.69041576$$

$$x=4-\sqrt{22}\approx -0.69041576$$

$$x=-1$$

Ngā Upane Otinga

Tangohia te 6 mai i ngā taha e rua.

$$x^{3}-7x^{2}-14x-6=0$$

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 -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.

$$x=-1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}-7x^{2}-14x-6 ki te x+1, kia riro ko x^{2}-8x-6. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$x^{2}-8x-6=0$$

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 -8 mō te b, me te -6 mō te c i te ture pūrua.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 1\left(-6\right)}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{8±2\sqrt{22}}{2}$$

Whakaotia te whārite x^{2}-8x-6=0 ina he tōrunga te ±, ina he tōraro te ±.

$$x=4-\sqrt{22} x=\sqrt{22}+4$$

Rārangitia ngā otinga katoa i kitea.

$$x=-1 x=4-\sqrt{22} x=\sqrt{22}+4$$