Whakaoti i te 1/3=m+m-1/m

$$\frac{1}{3}=m+\frac{m-1}{m}$$

Whakaoti mō m

$$m=\frac{\sqrt{10}-1}{3}\approx 0.72075922$$

$$m=\frac{-\sqrt{10}-1}{3}\approx -1.387425887$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tē taea kia ōrite te tāupe m ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3m, arā, te tauraro pātahi he tino iti rawa te kitea o 3,m.

$$m=3mm+3\left(m-1\right)$$

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

$$m=3m^{2}+3\left(m-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te m-1.

$$m=3m^{2}+3m-3$$

Tangohia te 3m^{2} mai i ngā taha e rua.

$$m-3m^{2}=3m-3$$

Tangohia te 3m mai i ngā taha e rua.

$$m-3m^{2}-3m=-3$$

Pahekotia te m me -3m, ka -2m.

$$-2m-3m^{2}=-3$$

Me tāpiri te 3 ki ngā taha e rua.

$$-2m-3m^{2}+3=0$$

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.

$$-3m^{2}-2m+3=0$$

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

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

Pūrua -2.

$$m=\frac{-\left(-2\right)±\sqrt{4-4\left(-3\right)\times 3}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$m=\frac{-\left(-2\right)±\sqrt{4+12\times 3}}{2\left(-3\right)}$$

Whakareatia 12 ki te 3.

$$m=\frac{-\left(-2\right)±\sqrt{4+36}}{2\left(-3\right)}$$

Tāpiri 4 ki te 36.

$$m=\frac{-\left(-2\right)±\sqrt{40}}{2\left(-3\right)}$$

Tuhia te pūtakerua o te 40.

$$m=\frac{-\left(-2\right)±2\sqrt{10}}{2\left(-3\right)}$$

Ko te tauaro o -2 ko 2.

$$m=\frac{2±2\sqrt{10}}{2\left(-3\right)}$$

Whakareatia 2 ki te -3.

$$m=\frac{2±2\sqrt{10}}{-6}$$

Nā, me whakaoti te whārite m=\frac{2±2\sqrt{10}}{-6} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{10}.

$$m=\frac{2\sqrt{10}+2}{-6}$$

Whakawehe 2+2\sqrt{10} ki te -6.

$$m=\frac{-\sqrt{10}-1}{3}$$

Nā, me whakaoti te whārite m=\frac{2±2\sqrt{10}}{-6} ina he tango te ±. Tango 2\sqrt{10} mai i 2.

$$m=\frac{2-2\sqrt{10}}{-6}$$

Whakawehe 2-2\sqrt{10} ki te -6.

$$m=\frac{\sqrt{10}-1}{3}$$

Kua oti te whārite te whakatau.

$$m=\frac{-\sqrt{10}-1}{3} m=\frac{\sqrt{10}-1}{3}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tē taea kia ōrite te tāupe m ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Me whakarea ngā taha e rua o te whārite ki te 3m, arā, te tauraro pātahi he tino iti rawa te kitea o 3,m.

$$m=3mm+3\left(m-1\right)$$

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

$$m=3m^{2}+3\left(m-1\right)$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3 ki te m-1.

$$m=3m^{2}+3m-3$$

Tangohia te 3m^{2} mai i ngā taha e rua.

$$m-3m^{2}=3m-3$$

Tangohia te 3m mai i ngā taha e rua.

$$m-3m^{2}-3m=-3$$

Pahekotia te m me -3m, ka -2m.

$$-2m-3m^{2}=-3$$

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.

$$-3m^{2}-2m=-3$$

Whakawehea ngā taha e rua ki te -3.

$$\frac{-3m^{2}-2m}{-3}=-\frac{3}{-3}$$

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

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

Whakawehe -2 ki te -3.

$$m^{2}+\frac{2}{3}m=-\frac{3}{-3}$$

Whakawehe -3 ki te -3.

$$m^{2}+\frac{2}{3}m=1$$

Whakawehea te \frac{2}{3}, te tau whakarea o te kīanga tau x, ki te 2 kia riro ai te \frac{1}{3}. Nā, tāpiria te pūrua o te \frac{1}{3} ki ngā taha e rua o te whārite. Mā konei e pūrua tika tonu ai te taha mauī o te whārite.

$$m^{2}+\frac{2}{3}m+\left(\frac{1}{3}\right)^{2}=1+\left(\frac{1}{3}\right)^{2}$$

Pūruatia \frac{1}{3} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$m^{2}+\frac{2}{3}m+\frac{1}{9}=1+\frac{1}{9}$$

Tāpiri 1 ki te \frac{1}{9}.

$$m^{2}+\frac{2}{3}m+\frac{1}{9}=\frac{10}{9}$$

Tauwehea m^{2}+\frac{2}{3}m+\frac{1}{9}. 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}.

$$\left(m+\frac{1}{3}\right)^{2}=\frac{10}{9}$$

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

$$\sqrt{\left(m+\frac{1}{3}\right)^{2}}=\sqrt{\frac{10}{9}}$$

Whakarūnātia.

$$m+\frac{1}{3}=\frac{\sqrt{10}}{3} m+\frac{1}{3}=-\frac{\sqrt{10}}{3}$$

Me tango \frac{1}{3} mai i ngā taha e rua o te whārite.

$$m=\frac{\sqrt{10}-1}{3} m=\frac{-\sqrt{10}-1}{3}$$