Whakaoti i te 9^6/9^3=a^6-3=

$$\frac { 9 ^ { 6 } } { 9 ^ { 3 } } = a ^ { 6 - 3 } =$$

Whakaoti mō a (complex solution)

$$a=\frac{-9\sqrt{3}i-9}{2}\approx -4.5-7.794228634i$$

$$a=9$$

$$a=\frac{-9+9\sqrt{3}i}{2}\approx -4.5+7.794228634i$$

Ngā Upane Otinga

Hei whakawehe ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga. Me tango te 3 i te 6 kia riro ai te 3.

$$9^{3}=a^{6-3}$$

Tātaihia te 9 mā te pū o 3, kia riro ko 729.

$$729=a^{6-3}$$

Tangohia te 3 i te 6, ka 3.

$$729=a^{3}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$a^{3}=729$$

Tangohia te 729 mai i ngā taha e rua.

$$a^{3}-729=0$$

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 -729, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±729,±243,±81,±27,±9,±3,±1$$

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.

$$a=9$$

Mā te whakatakotoranga Tauwehe, he tauwehe te a-k o te pūrau mō ia pūtake k. Whakawehea te a^{3}-729 ki te a-9, kia riro ko a^{2}+9a+81. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$a^{2}+9a+81=0$$

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 9 mō te b, me te 81 mō te c i te ture pūrua.

$$a=\frac{-9±\sqrt{9^{2}-4\times 1\times 81}}{2}$$

Mahia ngā tātaitai.

$$a=\frac{-9±\sqrt{-243}}{2}$$

Whakaotia te whārite a^{2}+9a+81=0 ina he tōrunga te ±, ina he tōraro te ±.

$$a=\frac{-9i\sqrt{3}-9}{2} a=\frac{-9+9i\sqrt{3}}{2}$$

Rārangitia ngā otinga katoa i kitea.

$$a=9 a=\frac{-9i\sqrt{3}-9}{2} a=\frac{-9+9i\sqrt{3}}{2}$$

Whakaoti mō a

$$a=9$$

Ngā Upane Otinga

Hei whakawehe ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga. Me tango te 3 i te 6 kia riro ai te 3.

$$9^{3}=a^{6-3}$$

Tātaihia te 9 mā te pū o 3, kia riro ko 729.

$$729=a^{6-3}$$

Tangohia te 3 i te 6, ka 3.

$$729=a^{3}$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$a^{3}=729$$

Tangohia te 729 mai i ngā taha e rua.

$$a^{3}-729=0$$

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 -729, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±729,±243,±81,±27,±9,±3,±1$$

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.

$$a=9$$

Mā te whakatakotoranga Tauwehe, he tauwehe te a-k o te pūrau mō ia pūtake k. Whakawehea te a^{3}-729 ki te a-9, kia riro ko a^{2}+9a+81. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$a^{2}+9a+81=0$$

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 9 mō te b, me te 81 mō te c i te ture pūrua.

$$a=\frac{-9±\sqrt{9^{2}-4\times 1\times 81}}{2}$$

Mahia ngā tātaitai.

$$a=\frac{-9±\sqrt{-243}}{2}$$

Tā te mea e kore te pūrua o tētahi tau tōraro e tautohutia ki te āpure tūturu, kāhore he rongoā.

$$a\in \emptyset$$

Rārangitia ngā otinga katoa i kitea.

$$a=9$$