Whakaoti i te (27/30)^3=(3.8*10^5/a)^2

$$( \frac { 27 } { 30 } ) ^ { 3 } = ( \frac { 3.8 \times 10 ^ { 5 } } { a } ) ^ { 2 }$$

Whakaoti mō a

$$a = -\frac{3800000 \sqrt{10}}{27} \approx -445061.300319994$$

$$a = \frac{3800000 \sqrt{10}}{27} \approx 445061.300319994$$

Ngā Upane mā te Kimi Pūtakerua

Whakahekea te hautanga \frac{27}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\left(\frac{9}{10}\right)^{3}=\left(\frac{3.8\times 10^{5}}{a}\right)^{2}$$

Tātaihia te \frac{9}{10} mā te pū o 3, kia riro ko \frac{729}{1000}.

$$\frac{729}{1000}=\left(\frac{3.8\times 10^{5}}{a}\right)^{2}$$

Tātaihia te 10 mā te pū o 5, kia riro ko 100000.

$$\frac{729}{1000}=\left(\frac{3.8\times 100000}{a}\right)^{2}$$

Whakareatia te 3.8 ki te 100000, ka 380000.

$$\frac{729}{1000}=\left(\frac{380000}{a}\right)^{2}$$

Kia whakarewa i te \frac{380000}{a} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{729}{1000}=\frac{380000^{2}}{a^{2}}$$

Tātaihia te 380000 mā te pū o 2, kia riro ko 144400000000.

$$\frac{729}{1000}=\frac{144400000000}{a^{2}}$$

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

$$\frac{144400000000}{a^{2}}=\frac{729}{1000}$$

Tē taea kia ōrite te tāupe a ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 1000a^{2}, arā, te tauraro pātahi he tino iti rawa te kitea o a^{2},1000.

$$1000\times 144400000000=729a^{2}$$

Whakareatia te 1000 ki te 144400000000, ka 144400000000000.

$$144400000000000=729a^{2}$$

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

$$729a^{2}=144400000000000$$

Whakawehea ngā taha e rua ki te 729.

$$a^{2}=\frac{144400000000000}{729}$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$a=\frac{3800000\sqrt{10}}{27} a=-\frac{3800000\sqrt{10}}{27}$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakahekea te hautanga \frac{27}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\left(\frac{9}{10}\right)^{3}=\left(\frac{3.8\times 10^{5}}{a}\right)^{2}$$

Tātaihia te \frac{9}{10} mā te pū o 3, kia riro ko \frac{729}{1000}.

$$\frac{729}{1000}=\left(\frac{3.8\times 10^{5}}{a}\right)^{2}$$

Tātaihia te 10 mā te pū o 5, kia riro ko 100000.

$$\frac{729}{1000}=\left(\frac{3.8\times 100000}{a}\right)^{2}$$

Whakareatia te 3.8 ki te 100000, ka 380000.

$$\frac{729}{1000}=\left(\frac{380000}{a}\right)^{2}$$

Kia whakarewa i te \frac{380000}{a} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

$$\frac{729}{1000}=\frac{380000^{2}}{a^{2}}$$

Tātaihia te 380000 mā te pū o 2, kia riro ko 144400000000.

$$\frac{729}{1000}=\frac{144400000000}{a^{2}}$$

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

$$\frac{144400000000}{a^{2}}=\frac{729}{1000}$$

Tangohia te \frac{729}{1000} mai i ngā taha e rua.

$$\frac{144400000000}{a^{2}}-\frac{729}{1000}=0$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o a^{2} me 1000 ko 1000a^{2}. Whakareatia \frac{144400000000}{a^{2}} ki te \frac{1000}{1000}. Whakareatia \frac{729}{1000} ki te \frac{a^{2}}{a^{2}}.

$$\frac{144400000000\times 1000}{1000a^{2}}-\frac{729a^{2}}{1000a^{2}}=0$$

Tā te mea he rite te tauraro o \frac{144400000000\times 1000}{1000a^{2}} me \frac{729a^{2}}{1000a^{2}}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{144400000000\times 1000-729a^{2}}{1000a^{2}}=0$$

Mahia ngā whakarea i roto o 144400000000\times 1000-729a^{2}.

$$\frac{144400000000000-729a^{2}}{1000a^{2}}=0$$

Tē taea kia ōrite te tāupe a ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te 1000a^{2}.

$$144400000000000-729a^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$-729a^{2}[phone]=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -729 mō a, 0 mō b, me 144400000000000 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-729\right)\times 144400000000000}}{2\left(-729\right)}$$

Pūrua 0.

$$a=\frac{0±\sqrt{-4\left(-729\right)\times 144400000000000}}{2\left(-729\right)}$$

Whakareatia -4 ki te -729.

$$a=\frac{0±\sqrt{2916\times 144400000000000}}{2\left(-729\right)}$$

Whakareatia 2916 ki te 144400000000000.

$$a=\frac{0±\sqrt{421070400000000000}}{2\left(-729\right)}$$

Tuhia te pūtakerua o te 421070400000000000.

$$a=\frac{0±205200000\sqrt{10}}{2\left(-729\right)}$$

Whakareatia 2 ki te -729.

$$a=\frac{0±205200000\sqrt{10}}{-1458}$$

Nā, me whakaoti te whārite a=\frac{0±205200000\sqrt{10}}{-1458} ina he tāpiri te ±.

$$a=-\frac{3800000\sqrt{10}}{27}$$

Nā, me whakaoti te whārite a=\frac{0±205200000\sqrt{10}}{-1458} ina he tango te ±.

$$a=\frac{3800000\sqrt{10}}{27}$$

Kua oti te whārite te whakatau.

$$a=-\frac{3800000\sqrt{10}}{27} a=\frac{3800000\sqrt{10}}{27}$$