Whakaoti i te (x-7)(x+3)(x^2-4)/(x+7)(x-1)=0

$$\frac { ( x - 7 ) ( x + 3 ) ( x ^ { 2 } - 4 ) } { ( x + 7 ) ( x - 1 ) } = 0$$

Whakaoti mō x

$$x=-3$$

$$x=7$$

$$x=-2$$

$$x=2$$

Ngā Upane Otinga

Tē taea kia ōrite te tāupe x ki tētahi o ngā uara -7,1 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te \left(x-1\right)\left(x+7\right).

$$\left(x-7\right)\left(x+3\right)\left(x^{2}-4\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x-7 ki te x+3 ka whakakotahi i ngā kupu rite.

$$\left(x^{2}-4x-21\right)\left(x^{2}-4\right)=0$$

Whakamahia te āhuatanga tuaritanga hei whakarea te x^{2}-4x-21 ki te x^{2}-4 ka whakakotahi i ngā kupu rite.

$$x^{4}-25x^{2}-4x^{3}+16x+84=0$$

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

$$x^{4}-4x^{3}-25x^{2}+16x+84=0$$

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

$$±84,±42,±28,±21,±14,±12,±7,±6,±4,±3,±2,±1$$

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}-4x^{3}-25x^{2}+16x+84 ki te x-2, kia riro ko x^{3}-2x^{2}-29x-42. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$x^{3}-2x^{2}-29x-42=0$$

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 -42, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±42,±21,±14,±7,±6,±3,±2,±1$$

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.

$$x=-2$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}-2x^{2}-29x-42 ki te x+2, kia riro ko x^{2}-4x-21. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$x^{2}-4x-21=0$$

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 -4 mō te b, me te -21 mō te c i te ture pūrua.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 1\left(-21\right)}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{4±10}{2}$$

Whakaotia te whārite x^{2}-4x-21=0 ina he tōrunga te ±, ina he tōraro te ±.

$$x=-3 x=7$$

Rārangitia ngā otinga katoa i kitea.

$$x=2 x=-2 x=-3 x=7$$