Whakaoti i te (6v-9)(2v+1)=7v^2-38-33

$$( 6 v - 9 ) ( 2 v + 1 ) = 7 v ^ { 2 } - 38 - 33$$

Whakaoti mō v

$$v=\frac{6+\sqrt{274}i}{5}\approx 1.2+3.310589071i$$

$$v=\frac{-\sqrt{274}i+6}{5}\approx 1.2-3.310589071i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 6v-9 ki te 2v+1 ka whakakotahi i ngā kupu rite.

$$12v^{2}-12v-9=7v^{2}-38-33$$

Tangohia te 33 i te -38, ka -71.

$$12v^{2}-12v-9=7v^{2}-71$$

Tangohia te 7v^{2} mai i ngā taha e rua.

$$12v^{2}-12v-9-7v^{2}=-71$$

Pahekotia te 12v^{2} me -7v^{2}, ka 5v^{2}.

$$5v^{2}-12v-9=-71$$

Me tāpiri te 71 ki ngā taha e rua.

$$5v^{2}-12v-9+71=0$$

Tāpirihia te -9 ki te 71, ka 62.

$$5v^{2}-12v+62=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 5 mō a, -12 mō b, me 62 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 5\times 62}}{2\times 5}$$

Pūrua -12.

$$v=\frac{-\left(-12\right)±\sqrt{144-4\times 5\times 62}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$v=\frac{-\left(-12\right)±\sqrt{144-20\times 62}}{2\times 5}$$

Whakareatia -20 ki te 62.

$$v=\frac{-\left(-12\right)±\sqrt{144-1240}}{2\times 5}$$

Tāpiri 144 ki te -1240.

$$v=\frac{-\left(-12\right)±\sqrt{-1096}}{2\times 5}$$

Tuhia te pūtakerua o te -1096.

$$v=\frac{-\left(-12\right)±2\sqrt{274}i}{2\times 5}$$

Ko te tauaro o -12 ko 12.

$$v=\frac{12±2\sqrt{274}i}{2\times 5}$$

Whakareatia 2 ki te 5.

$$v=\frac{12±2\sqrt{274}i}{10}$$

Nā, me whakaoti te whārite v=\frac{12±2\sqrt{274}i}{10} ina he tāpiri te ±. Tāpiri 12 ki te 2i\sqrt{274}.

$$v=\frac{12+2\sqrt{274}i}{10}$$

Whakawehe 12+2i\sqrt{274} ki te 10.

$$v=\frac{6+\sqrt{274}i}{5}$$

Nā, me whakaoti te whārite v=\frac{12±2\sqrt{274}i}{10} ina he tango te ±. Tango 2i\sqrt{274} mai i 12.

$$v=\frac{-2\sqrt{274}i+12}{10}$$

Whakawehe 12-2i\sqrt{274} ki te 10.

$$v=\frac{-\sqrt{274}i+6}{5}$$

Kua oti te whārite te whakatau.

$$v=\frac{6+\sqrt{274}i}{5} v=\frac{-\sqrt{274}i+6}{5}$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 6v-9 ki te 2v+1 ka whakakotahi i ngā kupu rite.

$$12v^{2}-12v-9=7v^{2}-38-33$$

Tangohia te 33 i te -38, ka -71.

$$12v^{2}-12v-9=7v^{2}-71$$

Tangohia te 7v^{2} mai i ngā taha e rua.

$$12v^{2}-12v-9-7v^{2}=-71$$

Pahekotia te 12v^{2} me -7v^{2}, ka 5v^{2}.

$$5v^{2}-12v-9=-71$$

Me tāpiri te 9 ki ngā taha e rua.

$$5v^{2}-12v=-71+9$$

Tāpirihia te -71 ki te 9, ka -62.

$$5v^{2}-12v=-62$$

Whakawehea ngā taha e rua ki te 5.

$$\frac{5v^{2}-12v}{5}=-\frac{62}{5}$$

Mā te whakawehe ki te 5 ka wetekia te whakareanga ki te 5.

$$v^{2}-\frac{12}{5}v=-\frac{62}{5}$$

Whakawehea te -\frac{12}{5}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -\frac{6}{5}. Nā, tāpiria te pūrua o te -\frac{6}{5} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$v^{2}-\frac{12}{5}v+\left(-\frac{6}{5}\right)^{2}=-\frac{62}{5}+\left(-\frac{6}{5}\right)^{2}$$

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

$$v^{2}-\frac{12}{5}v+\frac{36}{25}=-\frac{62}{5}+\frac{36}{25}$$

Tāpiri -\frac{62}{5} ki te \frac{36}{25} 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.

$$v^{2}-\frac{12}{5}v+\frac{36}{25}=-\frac{274}{25}$$

Tauwehea v^{2}-\frac{12}{5}v+\frac{36}{25}. 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}.

$$\left(v-\frac{6}{5}\right)^{2}=-\frac{274}{25}$$

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

$$\sqrt{\left(v-\frac{6}{5}\right)^{2}}=\sqrt{-\frac{274}{25}}$$

Whakarūnātia.

$$v-\frac{6}{5}=\frac{\sqrt{274}i}{5} v-\frac{6}{5}=-\frac{\sqrt{274}i}{5}$$

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

$$v=\frac{6+\sqrt{274}i}{5} v=\frac{-\sqrt{274}i+6}{5}$$