Whakaoti i te (3x-1)(x^2+4)=(3x-1)(8x-3)

$$( 3 x - 1 ) ( x ^ { 2 } + 4 ) = ( 3 x - 1 ) ( 8 x - 3 )$$

Whakaoti mō x

$$x=1$$

$$x=7$$

$$x=\frac{1}{3}\approx 0.333333333$$

Ngā Upane Otinga

Whakamahia te āhuatanga tohatoha hei whakarea te 3x-1 ki te x^{2}+4.

$$3x^{3}+12x-x^{2}-4=\left(3x-1\right)\left(8x-3\right)$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 3x-1 ki te 8x-3 ka whakakotahi i ngā kupu rite.

$$3x^{3}+12x-x^{2}-4=24x^{2}-17x+3$$

Tangohia te 24x^{2} mai i ngā taha e rua.

$$3x^{3}+12x-x^{2}-4-24x^{2}=-17x+3$$

Pahekotia te -x^{2} me -24x^{2}, ka -25x^{2}.

$$3x^{3}+12x-25x^{2}-4=-17x+3$$

Me tāpiri te 17x ki ngā taha e rua.

$$3x^{3}+12x-25x^{2}-4+17x=3$$

Pahekotia te 12x me 17x, ka 29x.

$$3x^{3}+29x-25x^{2}-4=3$$

Tangohia te 3 mai i ngā taha e rua.

$$3x^{3}+29x-25x^{2}-4-3=0$$

Tangohia te 3 i te -4, ka -7.

$$3x^{3}+29x-25x^{2}-7=0$$

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

$$3x^{3}-25x^{2}+29x-7=0$$

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 3. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±\frac{7}{3},±7,±\frac{1}{3},±1$$

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.

$$x=1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te 3x^{3}-25x^{2}+29x-7 ki te x-1, kia riro ko 3x^{2}-22x+7. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$3x^{2}-22x+7=0$$

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 3 mō te a, te -22 mō te b, me te 7 mō te c i te ture pūrua.

$$x=\frac{-\left(-22\right)±\sqrt{\left(-22\right)^{2}-4\times 3\times 7}}{2\times 3}$$

Mahia ngā tātaitai.

$$x=\frac{22±20}{6}$$

Whakaotia te whārite 3x^{2}-22x+7=0 ina he tōrunga te ±, ina he tōraro te ±.

$$x=\frac{1}{3} x=7$$

Rārangitia ngā otinga katoa i kitea.

$$x=1 x=\frac{1}{3} x=7$$