Whakaoti i te 3=v-10/v

$$3 = v - \frac { 10 } { v }$$

Whakaoti mō v

$$v=-2$$

$$v=5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

$$3v=vv-10$$

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

$$3v=v^{2}-10$$

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

$$3v-v^{2}=-10$$

Me tāpiri te 10 ki ngā taha e rua.

$$3v-v^{2}+10=0$$

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.

$$-v^{2}+3v+10=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 3 mō b, me 10 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{-3±\sqrt{3^{2}-4\left(-1\right)\times 10}}{2\left(-1\right)}$$

Pūrua 3.

$$v=\frac{-3±\sqrt{9-4\left(-1\right)\times 10}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$v=\frac{-3±\sqrt{9+4\times 10}}{2\left(-1\right)}$$

Whakareatia 4 ki te 10.

$$v=\frac{-3±\sqrt{9+40}}{2\left(-1\right)}$$

Tāpiri 9 ki te 40.

$$v=\frac{-3±\sqrt{49}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 49.

$$v=\frac{-3±7}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$v=\frac{-3±7}{-2}$$

Nā, me whakaoti te whārite v=\frac{-3±7}{-2} ina he tāpiri te ±. Tāpiri -3 ki te 7.

$$v=\frac{4}{-2}$$

Whakawehe 4 ki te -2.

$$v=-2$$

Nā, me whakaoti te whārite v=\frac{-3±7}{-2} ina he tango te ±. Tango 7 mai i -3.

$$v=-\frac{10}{-2}$$

Whakawehe -10 ki te -2.

$$v=5$$

Kua oti te whārite te whakatau.

$$v=-2 v=5$$

Ngā Upane mō te Whakaoti i te Pūrua

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

$$3v=vv-10$$

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

$$3v=v^{2}-10$$

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

$$3v-v^{2}=-10$$

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.

$$-v^{2}+3v=-10$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-v^{2}+3v}{-1}=-\frac{10}{-1}$$

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

$$v^{2}+\frac{3}{-1}v=-\frac{10}{-1}$$

Whakawehe 3 ki te -1.

$$v^{2}-3v=-\frac{10}{-1}$$

Whakawehe -10 ki te -1.

$$v^{2}-3v=10$$

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

$$v^{2}-3v+\left(-\frac{3}{2}\right)^{2}=10+\left(-\frac{3}{2}\right)^{2}$$

Pūruatia -\frac{3}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$v^{2}-3v+\frac{9}{4}=10+\frac{9}{4}$$

Tāpiri 10 ki te \frac{9}{4}.

$$v^{2}-3v+\frac{9}{4}=\frac{49}{4}$$

Tauwehea v^{2}-3v+\frac{9}{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}.

$$\left(v-\frac{3}{2}\right)^{2}=\frac{49}{4}$$

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

$$\sqrt{\left(v-\frac{3}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Whakarūnātia.

$$v-\frac{3}{2}=\frac{7}{2} v-\frac{3}{2}=-\frac{7}{2}$$

Me tāpiri \frac{3}{2} ki ngā taha e rua o te whārite.

$$v=5 v=-2$$