Whakaoti i te x^3+9x=1/2(18x+54)

$$x ^ { 3 } + 9 x = \frac { 1 } { 2 } ( 18 x + 54 )$$

Whakaoti mō x (complex solution)

$$x=\frac{-3\sqrt{3}i-3}{2}\approx -1.5-2.598076211i$$

$$x=3$$

$$x=\frac{-3+3\sqrt{3}i}{2}\approx -1.5+2.598076211i$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te 18x+54.

$$x^{3}+9x=9x+27$$

Tangohia te 9x mai i ngā taha e rua.

$$x^{3}+9x-9x=27$$

Pahekotia te 9x me -9x, ka 0.

$$x^{3}=27$$

Tangohia te 27 mai i ngā taha e rua.

$$x^{3}-27=0$$

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 -27, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±27,±9,±3,±1$$

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.

$$x=3$$

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

$$x^{2}+3x+9=0$$

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 3 mō te b, me te 9 mō te c i te ture pūrua.

$$x=\frac{-3±\sqrt{3^{2}-4\times 1\times 9}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{-3±\sqrt{-27}}{2}$$

Whakaotia te whārite x^{2}+3x+9=0 ina he tōrunga te ±, ina he tōraro te ±.

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

Rārangitia ngā otinga katoa i kitea.

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

Whakaoti mō x

$$x=3$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{1}{2} ki te 18x+54.

$$x^{3}+9x=9x+27$$

Tangohia te 9x mai i ngā taha e rua.

$$x^{3}+9x-9x=27$$

Pahekotia te 9x me -9x, ka 0.

$$x^{3}=27$$

Tangohia te 27 mai i ngā taha e rua.

$$x^{3}-27=0$$

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 -27, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±27,±9,±3,±1$$

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.

$$x=3$$

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

$$x^{2}+3x+9=0$$

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 3 mō te b, me te 9 mō te c i te ture pūrua.

$$x=\frac{-3±\sqrt{3^{2}-4\times 1\times 9}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{-3±\sqrt{-27}}{2}$$

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.

$$x=3$$