Whakaoti i te m^2-2m-3=1/2

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

Whakaoti mō m

$$m=\frac{3\sqrt{2}}{2}+1\approx 3.121320344$$

$$m=-\frac{3\sqrt{2}}{2}+1\approx -1.121320344$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

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

Me tango \frac{1}{2} mai i ngā taha e rua o te whārite.

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

Mā te tango i te \frac{1}{2} i a ia ake anō ka toe ko te 0.

$$m^{2}-2m-3-\frac{1}{2}=0$$

Tango \frac{1}{2} mai i -3.

$$m^{2}-2m-\frac{7}{2}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me -\frac{7}{2} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-\frac{7}{2}\right)}}{2}$$

Pūrua -2.

$$m=\frac{-\left(-2\right)±\sqrt{4-4\left(-\frac{7}{2}\right)}}{2}$$

Whakareatia -4 ki te -\frac{7}{2}.

$$m=\frac{-\left(-2\right)±\sqrt{4+14}}{2}$$

Tāpiri 4 ki te 14.

$$m=\frac{-\left(-2\right)±\sqrt{18}}{2}$$

Tuhia te pūtakerua o te 18.

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

Ko te tauaro o -2 ko 2.

$$m=\frac{2±3\sqrt{2}}{2}$$

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

$$m=\frac{3\sqrt{2}+2}{2}$$

Whakawehe 2+3\sqrt{2} ki te 2.

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

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

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

Whakawehe 2-3\sqrt{2} ki te 2.

$$m=-\frac{3\sqrt{2}}{2}+1$$

Kua oti te whārite te whakatau.

$$m=\frac{3\sqrt{2}}{2}+1 m=-\frac{3\sqrt{2}}{2}+1$$

Ngā Upane mō te Whakaoti i te Pūrua

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.

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

Me tāpiri 3 ki ngā taha e rua o te whārite.

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

Mā te tango i te -3 i a ia ake anō ka toe ko te 0.

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

Tango -3 mai i \frac{1}{2}.

$$m^{2}-2m=\frac{7}{2}$$

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.

$$m^{2}-2m+1=\frac{7}{2}+1$$

Tāpiri \frac{7}{2} ki te 1.

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

Tauwehea m^{2}-2m+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}.

$$\left(m-1\right)^{2}=\frac{9}{2}$$

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

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

Whakarūnātia.

$$m-1=\frac{3\sqrt{2}}{2} m-1=-\frac{3\sqrt{2}}{2}$$

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

$$m=\frac{3\sqrt{2}}{2}+1 m=-\frac{3\sqrt{2}}{2}+1$$