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

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

Whakaoti mō x

$$x=2$$

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$x=-2$$

Ngā Upane Otinga

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

$$2x^{3}-3x^{2}=4\left(2x-3\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 4 ki te 2x-3.

$$2x^{3}-3x^{2}=8x-12$$

Tangohia te 8x mai i ngā taha e rua.

$$2x^{3}-3x^{2}-8x=-12$$

Me tāpiri te 12 ki ngā taha e rua.

$$2x^{3}-3x^{2}-8x+12=0$$

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

$$±6,±12,±3,±2,±4,±\frac{3}{2},±1,±\frac{1}{2}$$

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 2x^{3}-3x^{2}-8x+12 ki te x-2, kia riro ko 2x^{2}+x-6. Whakaotihia te whārite ina ōrite te hua ki te 0.

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

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 2 mō te a, te 1 mō te b, me te -6 mō te c i te ture pūrua.

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

Mahia ngā tātaitai.

$$x=\frac{-1±7}{4}$$

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

$$x=-2 x=\frac{3}{2}$$

Rārangitia ngā otinga katoa i kitea.

$$x=2 x=-2 x=\frac{3}{2}$$