Whakaoti i te 9q^2-7q+1=0

$$9 q ^ { 2 } - 7 q + 1 = 0$$

Whakaoti mō q

$$q=\frac{\sqrt{13}+7}{18}\approx 0.589197293$$

$$q=\frac{7-\sqrt{13}}{18}\approx 0.188580485$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$9q^{2}-7q+1=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 9 mō a, -7 mō b, me 1 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 9}}{2\times 9}$$

Pūrua -7.

$$q=\frac{-\left(-7\right)±\sqrt{49-4\times 9}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$q=\frac{-\left(-7\right)±\sqrt{49-36}}{2\times 9}$$

Tāpiri 49 ki te -36.

$$q=\frac{-\left(-7\right)±\sqrt{13}}{2\times 9}$$

Ko te tauaro o -7 ko 7.

$$q=\frac{7±\sqrt{13}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$q=\frac{7±\sqrt{13}}{18}$$

Nā, me whakaoti te whārite q=\frac{7±\sqrt{13}}{18} ina he tāpiri te ±. Tāpiri 7 ki te \sqrt{13}.

$$q=\frac{\sqrt{13}+7}{18}$$

Nā, me whakaoti te whārite q=\frac{7±\sqrt{13}}{18} ina he tango te ±. Tango \sqrt{13} mai i 7.

$$q=\frac{7-\sqrt{13}}{18}$$

Kua oti te whārite te whakatau.

$$q=\frac{\sqrt{13}+7}{18} q=\frac{7-\sqrt{13}}{18}$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

$$9q^{2}-7q+1=0$$

Me tango 1 mai i ngā taha e rua o te whārite.

$$9q^{2}-7q+1-1=-1$$

Mā te tango i te 1 i a ia ake anō ka toe ko te 0.

$$9q^{2}-7q=-1$$

Whakawehea ngā taha e rua ki te 9.

$$\frac{9q^{2}-7q}{9}=-\frac{1}{9}$$

Mā te whakawehe ki te 9 ka wetekia te whakareanga ki te 9.

$$q^{2}-\frac{7}{9}q=-\frac{1}{9}$$

Whakawehea te -\frac{7}{9}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{7}{18}. Nā, tāpiria te pūrua o te -\frac{7}{18} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$q^{2}-\frac{7}{9}q+\left(-\frac{7}{18}\right)^{2}=-\frac{1}{9}+\left(-\frac{7}{18}\right)^{2}$$

Pūruatia -\frac{7}{18} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$q^{2}-\frac{7}{9}q+\frac{49}{324}=-\frac{1}{9}+\frac{49}{324}$$

Tāpiri -\frac{1}{9} ki te \frac{49}{324} 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.

$$q^{2}-\frac{7}{9}q+\frac{49}{324}=\frac{13}{324}$$

Tauwehea q^{2}-\frac{7}{9}q+\frac{49}{324}. 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}.

$$\left(q-\frac{7}{18}\right)^{2}=\frac{13}{324}$$

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

$$\sqrt{\left(q-\frac{7}{18}\right)^{2}}=\sqrt{\frac{13}{324}}$$

Whakarūnātia.

$$q-\frac{7}{18}=\frac{\sqrt{13}}{18} q-\frac{7}{18}=-\frac{\sqrt{13}}{18}$$

Me tāpiri \frac{7}{18} ki ngā taha e rua o te whārite.

$$q=\frac{\sqrt{13}+7}{18} q=\frac{7-\sqrt{13}}{18}$$