Whakaoti i te 4/a=15-9a

$$\frac { 4 } { a } = 15 - 9 a$$

Whakaoti mō a

$$a=\frac{1}{3}\approx 0.333333333$$

$$a = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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 a.

$$4=a\times 15-9aa$$

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

$$4=a\times 15-9a^{2}$$

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

$$a\times 15-9a^{2}=4$$

Tangohia te 4 mai i ngā taha e rua.

$$a\times 15-9a^{2}-4=0$$

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.

$$-9a^{2}+15a-4=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -9 mō a, 15 mō b, me -4 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-15±\sqrt{15^{2}-4\left(-9\right)\left(-4\right)}}{2\left(-9\right)}$$

Pūrua 15.

$$a=\frac{-15±\sqrt{225-4\left(-9\right)\left(-4\right)}}{2\left(-9\right)}$$

Whakareatia -4 ki te -9.

$$a=\frac{-15±\sqrt{225+36\left(-4\right)}}{2\left(-9\right)}$$

Whakareatia 36 ki te -4.

$$a=\frac{-15±\sqrt{225-144}}{2\left(-9\right)}$$

Tāpiri 225 ki te -144.

$$a=\frac{-15±\sqrt{81}}{2\left(-9\right)}$$

Tuhia te pūtakerua o te 81.

$$a=\frac{-15±9}{2\left(-9\right)}$$

Whakareatia 2 ki te -9.

$$a=\frac{-15±9}{-18}$$

Nā, me whakaoti te whārite a=\frac{-15±9}{-18} ina he tāpiri te ±. Tāpiri -15 ki te 9.

$$a=-\frac{6}{-18}$$

Whakahekea te hautanga \frac{-6}{-18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$a=\frac{1}{3}$$

Nā, me whakaoti te whārite a=\frac{-15±9}{-18} ina he tango te ±. Tango 9 mai i -15.

$$a=-\frac{24}{-18}$$

Whakahekea te hautanga \frac{-24}{-18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$a=\frac{4}{3}$$

Kua oti te whārite te whakatau.

$$a=\frac{1}{3} a=\frac{4}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

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 a.

$$4=a\times 15-9aa$$

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

$$4=a\times 15-9a^{2}$$

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

$$a\times 15-9a^{2}=4$$

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.

$$-9a^{2}+15a=4$$

Whakawehea ngā taha e rua ki te -9.

$$\frac{-9a^{2}+15a}{-9}=\frac{4}{-9}$$

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

$$a^{2}+\frac{15}{-9}a=\frac{4}{-9}$$

Whakahekea te hautanga \frac{15}{-9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$a^{2}-\frac{5}{3}a=\frac{4}{-9}$$

Whakawehe 4 ki te -9.

$$a^{2}-\frac{5}{3}a=-\frac{4}{9}$$

Whakawehea te -\frac{5}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{5}{6}. Nā, tāpiria te pūrua o te -\frac{5}{6} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$a^{2}-\frac{5}{3}a+\left(-\frac{5}{6}\right)^{2}=-\frac{4}{9}+\left(-\frac{5}{6}\right)^{2}$$

Pūruatia -\frac{5}{6} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$a^{2}-\frac{5}{3}a+\frac{25}{36}=-\frac{4}{9}+\frac{25}{36}$$

Tāpiri -\frac{4}{9} ki te \frac{25}{36} 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.

$$a^{2}-\frac{5}{3}a+\frac{25}{36}=\frac{1}{4}$$

Tauwehea a^{2}-\frac{5}{3}a+\frac{25}{36}. 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}.

$$\left(a-\frac{5}{6}\right)^{2}=\frac{1}{4}$$

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

$$\sqrt{\left(a-\frac{5}{6}\right)^{2}}=\sqrt{\frac{1}{4}}$$

Whakarūnātia.

$$a-\frac{5}{6}=\frac{1}{2} a-\frac{5}{6}=-\frac{1}{2}$$

Me tāpiri \frac{5}{6} ki ngā taha e rua o te whārite.

$$a=\frac{4}{3} a=\frac{1}{3}$$