Whakaoti i te 3v^2-15=6v

$$3 v ^ { 2 } - 15 = 6 v$$

Whakaoti mō v

$$v=\sqrt{6}+1\approx 3.449489743$$

$$v=1-\sqrt{6}\approx -1.449489743$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te 6v mai i ngā taha e rua.

$$3v^{2}-15-6v=0$$

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.

$$3v^{2}-6v-15=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 3 mō a, -6 mō b, me -15 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$v=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 3\left(-15\right)}}{2\times 3}$$

Pūrua -6.

$$v=\frac{-\left(-6\right)±\sqrt{36-4\times 3\left(-15\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$v=\frac{-\left(-6\right)±\sqrt{36-12\left(-15\right)}}{2\times 3}$$

Whakareatia -12 ki te -15.

$$v=\frac{-\left(-6\right)±\sqrt{36+180}}{2\times 3}$$

Tāpiri 36 ki te 180.

$$v=\frac{-\left(-6\right)±\sqrt{216}}{2\times 3}$$

Tuhia te pūtakerua o te 216.

$$v=\frac{-\left(-6\right)±6\sqrt{6}}{2\times 3}$$

Ko te tauaro o -6 ko 6.

$$v=\frac{6±6\sqrt{6}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$v=\frac{6±6\sqrt{6}}{6}$$

Nā, me whakaoti te whārite v=\frac{6±6\sqrt{6}}{6} ina he tāpiri te ±. Tāpiri 6 ki te 6\sqrt{6}.

$$v=\frac{6\sqrt{6}+6}{6}$$

Whakawehe 6+6\sqrt{6} ki te 6.

$$v=\sqrt{6}+1$$

Nā, me whakaoti te whārite v=\frac{6±6\sqrt{6}}{6} ina he tango te ±. Tango 6\sqrt{6} mai i 6.

$$v=\frac{6-6\sqrt{6}}{6}$$

Whakawehe 6-6\sqrt{6} ki te 6.

$$v=1-\sqrt{6}$$

Kua oti te whārite te whakatau.

$$v=\sqrt{6}+1 v=1-\sqrt{6}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te 6v mai i ngā taha e rua.

$$3v^{2}-15-6v=0$$

Me tāpiri te 15 ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$3v^{2}-6v=15$$

Whakawehea ngā taha e rua ki te 3.

$$\frac{3v^{2}-6v}{3}=\frac{15}{3}$$

Mā te whakawehe ki te 3 ka wetekia te whakareanga ki te 3.

$$v^{2}+\left(-\frac{6}{3}\right)v=\frac{15}{3}$$

Whakawehe -6 ki te 3.

$$v^{2}-2v=\frac{15}{3}$$

Whakawehe 15 ki te 3.

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

Whakawehea te -2, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te -1. Nā, tāpiria te pūrua o te -1 ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$v^{2}-2v+1=5+1$$

Tāpiri 5 ki te 1.

$$v^{2}-2v+1=6$$

Tauwehea v^{2}-2v+1. 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}.

$$\left(v-1\right)^{2}=6$$

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

$$\sqrt{\left(v-1\right)^{2}}=\sqrt{6}$$

Whakarūnātia.

$$v-1=\sqrt{6} v-1=-\sqrt{6}$$

Me tāpiri 1 ki ngā taha e rua o te whārite.

$$v=\sqrt{6}+1 v=1-\sqrt{6}$$