Whakaoti i te E-1317=683:E=

$$E - 1317 = 683 : E =$$

Whakaoti mō E

$$E = \frac{\sqrt{1737221} + 1317}{2} \approx 1317.518398833$$

$$E=\frac{1317-\sqrt{1737221}}{2}\approx -0.518398833$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe E ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te E.

$$EE+E\left(-1317\right)=683$$

Whakareatia te E ki te E, ka E^{2}.

$$E^{2}+E\left(-1317\right)=683$$

Tangohia te 683 mai i ngā taha e rua.

$$E^{2}+E\left(-1317\right)-683=0$$

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.

$$E^{2}-1317E-683=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -1317 mō b, me -683 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$E=\frac{-\left(-1317\right)±\sqrt{\left(-1317\right)^{2}-4\left(-683\right)}}{2}$$

Pūrua -1317.

$$E=\frac{-\left(-1317\right)±\sqrt{1734489-4\left(-683\right)}}{2}$$

Whakareatia -4 ki te -683.

$$E=\frac{-\left(-1317\right)±\sqrt{1734489+2732}}{2}$$

Tāpiri 1734489 ki te 2732.

$$E=\frac{-\left(-1317\right)±\sqrt{1737221}}{2}$$

Ko te tauaro o -1317 ko 1317.

$$E=\frac{1317±\sqrt{1737221}}{2}$$

Nā, me whakaoti te whārite E=\frac{1317±\sqrt{1737221}}{2} ina he tāpiri te ±. Tāpiri 1317 ki te \sqrt{1737221}.

$$E=\frac{\sqrt{1737221}+1317}{2}$$

Nā, me whakaoti te whārite E=\frac{1317±\sqrt{1737221}}{2} ina he tango te ±. Tango \sqrt{1737221} mai i 1317.

$$E=\frac{1317-\sqrt{1737221}}{2}$$

Kua oti te whārite te whakatau.

$$E=\frac{\sqrt{1737221}+1317}{2} E=\frac{1317-\sqrt{1737221}}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe E ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te E.

$$EE+E\left(-1317\right)=683$$

Whakareatia te E ki te E, ka E^{2}.

$$E^{2}+E\left(-1317\right)=683$$

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.

$$E^{2}-1317E=683$$

Whakawehea te -1317, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{1317}{2}. Nā, tāpiria te pūrua o te -\frac{1317}{2} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$E^{2}-1317E+\left(-\frac{1317}{2}\right)^{2}=683+\left(-\frac{1317}{2}\right)^{2}$$

Pūruatia -\frac{1317}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$E^{2}-1317E+\frac{1734489}{4}=683+\frac{1734489}{4}$$

Tāpiri 683 ki te \frac{1734489}{4}.

$$E^{2}-1317E+\frac{1734489}{4}=\frac{1737221}{4}$$

Tauwehea E^{2}-1317E+\frac{1734489}{4}. 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}.

$$\left(E-\frac{1317}{2}\right)^{2}=\frac{1737221}{4}$$

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

$$\sqrt{\left(E-\frac{1317}{2}\right)^{2}}=\sqrt{\frac{1737221}{4}}$$

Whakarūnātia.

$$E-\frac{1317}{2}=\frac{\sqrt{1737221}}{2} E-\frac{1317}{2}=-\frac{\sqrt{1737221}}{2}$$

Me tāpiri \frac{1317}{2} ki ngā taha e rua o te whārite.

$$E=\frac{\sqrt{1737221}+1317}{2} E=\frac{1317-\sqrt{1737221}}{2}$$