Whakaoti i te x^2/10=100/x

$$\frac{ { x }^{ 2 } }{ 10 } = \frac{ 100 }{ x }$$

Whakaoti mō x (complex solution)

$$x=-5\sqrt{3}i-5\approx -5-8.660254038i$$

$$x=10$$

$$x=-5+5\sqrt{3}i\approx -5+8.660254038i$$

Ngā Upane Otinga

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 10x, arā, te tauraro pātahi he tino iti rawa te kitea o 10,x.

$$xx^{2}=10\times 100$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

$$x^{3}=10\times 100$$

Whakareatia te 10 ki te 100, ka 1000.

$$x^{3}=1000$$

Tangohia te 1000 mai i ngā taha e rua.

$$x^{3}-1000=0$$

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 -1000, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±1000,±500,±250,±200,±125,±100,±50,±40,±25,±20,±10,±8,±5,±4,±2,±1$$

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.

$$x=10$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}-1000 ki te x-10, kia riro ko x^{2}+10x+100. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$x^{2}+10x+100=0$$

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 10 mō te b, me te 100 mō te c i te ture pūrua.

$$x=\frac{-10±\sqrt{10^{2}-4\times 1\times 100}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{-10±\sqrt{-300}}{2}$$

Whakaotia te whārite x^{2}+10x+100=0 ina he tōrunga te ±, ina he tōraro te ±.

$$x=-5i\sqrt{3}-5 x=-5+5i\sqrt{3}$$

Rārangitia ngā otinga katoa i kitea.

$$x=10 x=-5i\sqrt{3}-5 x=-5+5i\sqrt{3}$$

Whakaoti mō x

$$x=10$$

Ngā Upane Otinga

Tē taea kia ōrite te tāupe x ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 10x, arā, te tauraro pātahi he tino iti rawa te kitea o 10,x.

$$xx^{2}=10\times 100$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

$$x^{3}=10\times 100$$

Whakareatia te 10 ki te 100, ka 1000.

$$x^{3}=1000$$

Tangohia te 1000 mai i ngā taha e rua.

$$x^{3}-1000=0$$

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 -1000, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±1000,±500,±250,±200,±125,±100,±50,±40,±25,±20,±10,±8,±5,±4,±2,±1$$

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.

$$x=10$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}-1000 ki te x-10, kia riro ko x^{2}+10x+100. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$x^{2}+10x+100=0$$

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 10 mō te b, me te 100 mō te c i te ture pūrua.

$$x=\frac{-10±\sqrt{10^{2}-4\times 1\times 100}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{-10±\sqrt{-300}}{2}$$

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.

$$x=10$$