Whakaoti i te -2x+3x^3=20

$$- 2 x + 3 x ^ { 3 } = 20$$

Whakaoti mō x (complex solution)

$$x=-\frac{\sqrt{21}i}{3}-1\approx -1-1.527525232i$$

$$x=2$$

$$x=\frac{\sqrt{21}i}{3}-1\approx -1+1.527525232i$$

Ngā Upane Otinga

Tangohia te 20 mai i ngā taha e rua.

$$-2x+3x^{3}-20=0$$

Hurinahatia te whārite ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$3x^{3}-2x-20=0$$

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 -20, ā, ka wehea e q te whakarea arahanga 3. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±\frac{20}{3},±20,±\frac{10}{3},±10,±\frac{5}{3},±5,±\frac{4}{3},±4,±\frac{2}{3},±2,±\frac{1}{3},±1$$

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.

$$x=2$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te 3x^{3}-2x-20 ki te x-2, kia riro ko 3x^{2}+6x+10. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$3x^{2}+6x+10=0$$

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 3 mō te a, te 6 mō te b, me te 10 mō te c i te ture pūrua.

$$x=\frac{-6±\sqrt{6^{2}-4\times 3\times 10}}{2\times 3}$$

Mahia ngā tātaitai.

$$x=\frac{-6±\sqrt{-84}}{6}$$

Whakaotia te whārite 3x^{2}+6x+10=0 ina he tōrunga te ±, ina he tōraro te ±.

$$x=-\frac{\sqrt{21}i}{3}-1 x=\frac{\sqrt{21}i}{3}-1$$

Rārangitia ngā otinga katoa i kitea.

$$x=2 x=-\frac{\sqrt{21}i}{3}-1 x=\frac{\sqrt{21}i}{3}-1$$

Whakaoti mō x

$$x=2$$

Ngā Upane Otinga

Tangohia te 20 mai i ngā taha e rua.

$$-2x+3x^{3}-20=0$$

Hurinahatia te whārite ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$3x^{3}-2x-20=0$$

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 -20, ā, ka wehea e q te whakarea arahanga 3. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±\frac{20}{3},±20,±\frac{10}{3},±10,±\frac{5}{3},±5,±\frac{4}{3},±4,±\frac{2}{3},±2,±\frac{1}{3},±1$$

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.

$$x=2$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te 3x^{3}-2x-20 ki te x-2, kia riro ko 3x^{2}+6x+10. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$3x^{2}+6x+10=0$$

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 3 mō te a, te 6 mō te b, me te 10 mō te c i te ture pūrua.

$$x=\frac{-6±\sqrt{6^{2}-4\times 3\times 10}}{2\times 3}$$

Mahia ngā tātaitai.

$$x=\frac{-6±\sqrt{-84}}{6}$$

Tā te mea e kore te pūrua o tētahi tau tōraro e tautohutia ki te āpure tūturu, kāhore he rongoā.

$$x\in \emptyset$$

Rārangitia ngā otinga katoa i kitea.

$$x=2$$