Whakaoti i te (x+6)(x+3)(x-1)(x-2)=12x^2

$$(x+6)(x+3)(x-1)(x-2)=12 { x }^{ 2 }$$

Whakaoti mō x

$$x=\frac{\sqrt{73}-7}{2}\approx 0.772001873$$

$$x=\frac{-\sqrt{73}-7}{2}\approx -7.772001873$$

$$x=3$$

$$x=-2$$

Ngā Upane Otinga

Whakamahia te āhuatanga tuaritanga hei whakarea te x+6 ki te x+3 ka whakakotahi i ngā kupu rite.

$$\left(x^{2}+9x+18\right)\left(x-1\right)\left(x-2\right)=12x^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x^{2}+9x+18 ki te x-1 ka whakakotahi i ngā kupu rite.

$$\left(x^{3}+8x^{2}+9x-18\right)\left(x-2\right)=12x^{2}$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x^{3}+8x^{2}+9x-18 ki te x-2 ka whakakotahi i ngā kupu rite.

$$x^{4}+6x^{3}-7x^{2}-36x+36=12x^{2}$$

Tangohia te 12x^{2} mai i ngā taha e rua.

$$x^{4}+6x^{3}-7x^{2}-36x+36-12x^{2}=0$$

Pahekotia te -7x^{2} me -12x^{2}, ka -19x^{2}.

$$x^{4}+6x^{3}-19x^{2}-36x+36=0$$

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

$$±36,±18,±12,±9,±6,±4,±3,±2,±1$$

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.

$$x=-2$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{4}+6x^{3}-19x^{2}-36x+36 ki te x+2, kia riro ko x^{3}+4x^{2}-27x+18. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$x^{3}+4x^{2}-27x+18=0$$

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

$$±18,±9,±6,±3,±2,±1$$

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.

$$x=3$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}+4x^{2}-27x+18 ki te x-3, kia riro ko x^{2}+7x-6. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$x^{2}+7x-6=0$$

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 1 mō te a, te 7 mō te b, me te -6 mō te c i te ture pūrua.

$$x=\frac{-7±\sqrt{7^{2}-4\times 1\left(-6\right)}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{-7±\sqrt{73}}{2}$$

Whakaotia te whārite x^{2}+7x-6=0 ina he tōrunga te ±, ina he tōraro te ±.

$$x=\frac{-\sqrt{73}-7}{2} x=\frac{\sqrt{73}-7}{2}$$

Rārangitia ngā otinga katoa i kitea.

$$x=-2 x=3 x=\frac{-\sqrt{73}-7}{2} x=\frac{\sqrt{73}-7}{2}$$