Whakaoti i te 473^-4=x^2/64-x

$${ 473 }^{ -4 } = \frac{ { x }^{ 2 } }{ 64-x }$$

Whakaoti mō x

$$x=\frac{\sqrt{12813994352897}-1}{100109330882}\approx 0.000035758$$

$$x=\frac{-\sqrt{12813994352897}-1}{100109330882}\approx -0.000035758$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe x ki 64 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+64.

$$\left(-x+64\right)\times 473^{-4}=x^{2}$$

Tātaihia te 473 mā te pū o -4, kia riro ko \frac{1}{50054665441}.

$$\left(-x+64\right)\times \frac{1}{50054665441}=x^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te -x+64 ki te \frac{1}{50054665441}.

$$-\frac{1}{50054665441}x+\frac{64}{50054665441}=x^{2}$$

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

$$-\frac{1}{50054665441}x+\frac{64}{50054665441}-x^{2}=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$-x^{2}-\frac{1}{50054665441}x+\frac{64}{50054665441}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, -\frac{1}{50054665441} mō b, me \frac{64}{50054665441} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\left(-\frac{1}{50054665441}\right)^{2}-4\left(-1\right)\times \frac{64}{50054665441}}}{2\left(-1\right)}$$

Pūruatia -\frac{1}{50054665441} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\frac{1}{2505469532410439724481}-4\left(-1\right)\times \frac{64}{50054665441}}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\frac{1}{2505469532410439724481}+4\times \frac{64}{50054665441}}}{2\left(-1\right)}$$

Whakareatia 4 ki te \frac{64}{50054665441}.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\frac{1}{2505469532410439724481}+\frac{256}{50054665441}}}{2\left(-1\right)}$$

Tāpiri \frac{1}{2505469532410439724481} ki te \frac{256}{50054665441} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\sqrt{\frac{12813994352897}{2505469532410439724481}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te \frac{12813994352897}{2505469532410439724481}.

$$x=\frac{-\left(-\frac{1}{50054665441}\right)±\frac{\sqrt{12813994352897}}{50054665441}}{2\left(-1\right)}$$

Ko te tauaro o -\frac{1}{50054665441} ko \frac{1}{50054665441}.

$$x=\frac{\frac{1}{50054665441}±\frac{\sqrt{12813994352897}}{50054665441}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{\frac{1}{50054665441}±\frac{\sqrt{12813994352897}}{50054665441}}{-2}$$

Nā, me whakaoti te whārite x=\frac{\frac{1}{50054665441}±\frac{\sqrt{12813994352897}}{50054665441}}{-2} ina he tāpiri te ±. Tāpiri \frac{1}{50054665441} ki te \frac{\sqrt{12813994352897}}{50054665441}.

$$x=\frac{\sqrt{12813994352897}+1}{-2\times 50054665441}$$

Whakawehe \frac{1+\sqrt{12813994352897}}{50054665441} ki te -2.

$$x=\frac{-\sqrt{12813994352897}-1}{100109330882}$$

Nā, me whakaoti te whārite x=\frac{\frac{1}{50054665441}±\frac{\sqrt{12813994352897}}{50054665441}}{-2} ina he tango te ±. Tango \frac{\sqrt{12813994352897}}{50054665441} mai i \frac{1}{50054665441}.

$$x=\frac{1-\sqrt{12813994352897}}{-2\times 50054665441}$$

Whakawehe \frac{1-\sqrt{12813994352897}}{50054665441} ki te -2.

$$x=\frac{\sqrt{12813994352897}-1}{100109330882}$$

Kua oti te whārite te whakatau.

$$x=\frac{-\sqrt{12813994352897}-1}{100109330882} x=\frac{\sqrt{12813994352897}-1}{100109330882}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe x ki 64 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te -x+64.

$$\left(-x+64\right)\times 473^{-4}=x^{2}$$

Tātaihia te 473 mā te pū o -4, kia riro ko \frac{1}{50054665441}.

$$\left(-x+64\right)\times \frac{1}{50054665441}=x^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te -x+64 ki te \frac{1}{50054665441}.

$$-\frac{1}{50054665441}x+\frac{64}{50054665441}=x^{2}$$

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

$$-\frac{1}{50054665441}x+\frac{64}{50054665441}-x^{2}=0$$

Tangohia te \frac{64}{50054665441} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-\frac{1}{50054665441}x-x^{2}=-\frac{64}{50054665441}$$

Ko ngā whārite pūrua pēnei i tēnei nā ka taea te whakaoti mā te whakaoti i te pūrua. Hei whakaoti i te pūrua, ko te whārite me mātua tuhi ki te āhua x^{2}+bx=c.

$$-x^{2}-\frac{1}{50054665441}x=-\frac{64}{50054665441}$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-x^{2}-\frac{1}{50054665441}x}{-1}=-\frac{\frac{64}{50054665441}}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$x^{2}+\left(-\frac{\frac{1}{50054665441}}{-1}\right)x=-\frac{\frac{64}{50054665441}}{-1}$$

Whakawehe -\frac{1}{50054665441} ki te -1.

$$x^{2}+\frac{1}{50054665441}x=-\frac{\frac{64}{50054665441}}{-1}$$

Whakawehe -\frac{64}{50054665441} ki te -1.

$$x^{2}+\frac{1}{50054665441}x=\frac{64}{50054665441}$$

Whakawehea te \frac{1}{50054665441}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{100109330882}. Nā, tāpiria te pūrua o te \frac{1}{100109330882} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$x^{2}+\frac{1}{50054665441}x+\left(\frac{1}{100109330882}\right)^{2}=\frac{64}{50054665441}+\left(\frac{1}{100109330882}\right)^{2}$$

Pūruatia \frac{1}{100109330882} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$x^{2}+\frac{1}{50054665441}x+\frac{1}{10021878129641758897924}=\frac{64}{50054665441}+\frac{1}{10021878129641758897924}$$

Tāpiri \frac{64}{50054665441} ki te \frac{1}{10021878129641758897924} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$x^{2}+\frac{1}{50054665441}x+\frac{1}{10021878129641758897924}=\frac{12813994352897}{10021878129641758897924}$$

Tauwehea x^{2}+\frac{1}{50054665441}x+\frac{1}{10021878129641758897924}. Ko te tikanga pūnoa, ina ko x^{2}+bx+c he pūrua tika pūrua tika pū, ka taea taua mea te tauwehea i ngā wā katoa hei \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{1}{100109330882}\right)^{2}=\frac{12813994352897}{10021878129641758897924}$$

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

$$\sqrt{\left(x+\frac{1}{100109330882}\right)^{2}}=\sqrt{\frac{12813994352897}{10021878129641758897924}}$$

Whakarūnātia.

$$x+\frac{1}{100109330882}=\frac{\sqrt{12813994352897}}{100109330882} x+\frac{1}{100109330882}=-\frac{\sqrt{12813994352897}}{100109330882}$$

Me tango \frac{1}{100109330882} mai i ngā taha e rua o te whārite.

$$x=\frac{\sqrt{12813994352897}-1}{100109330882} x=\frac{-\sqrt{12813994352897}-1}{100109330882}$$