Whakaoti i te 3=(2x^2+1)x

$$3 = ( 2 x ^ { 2 } + 1 ) x$$

Whakaoti mō x (complex solution)

$$x=\frac{-\sqrt{5}i-1}{2}\approx -0.5-1.118033989i$$

$$x=\frac{-1+\sqrt{5}i}{2}\approx -0.5+1.118033989i$$

$$x=1$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 2x^{2}+1 ki te x.

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

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Tangohia te 3 mai i ngā taha e rua.

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

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 -3, ā, ka wehea e q te whakarea arahanga 2. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±\frac{3}{2},±3,±\frac{1}{2},±1$$

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 2x^{3}+x-3 ki te x-1, kia riro ko 2x^{2}+2x+3. Whakaotihia te whārite ina ōrite te hua ki te 0.

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

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 2 mō te a, te 2 mō te b, me te 3 mō te c i te ture pūrua.

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

Mahia ngā tātaitai.

$$x=\frac{-2±\sqrt{-20}}{4}$$

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

$$x=\frac{-\sqrt{5}i-1}{2} x=\frac{-1+\sqrt{5}i}{2}$$

Rārangitia ngā otinga katoa i kitea.

$$x=1 x=\frac{-\sqrt{5}i-1}{2} x=\frac{-1+\sqrt{5}i}{2}$$

Whakaoti mō x

$$x=1$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 2x^{2}+1 ki te x.

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

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

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

Tangohia te 3 mai i ngā taha e rua.

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

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 -3, ā, ka wehea e q te whakarea arahanga 2. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±\frac{3}{2},±3,±\frac{1}{2},±1$$

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 2x^{3}+x-3 ki te x-1, kia riro ko 2x^{2}+2x+3. Whakaotihia te whārite ina ōrite te hua ki te 0.

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

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 2 mō te a, te 2 mō te b, me te 3 mō te c i te ture pūrua.

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

Mahia ngā tātaitai.

$$x=\frac{-2±\sqrt{-20}}{4}$$

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.

$$x=1$$