Whakaoti i te m^2-2m+5=0

$${ m }^{ 2 } -2m+5 = 0$$

Whakaoti mō m

$$m=1+2i$$

$$m=1-2i$$

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.

$$m^{2}-2m+5=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me 5 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Pūrua -2.

$$m=\frac{-\left(-2\right)±\sqrt{4-4\times 5}}{2}$$

Whakareatia -4 ki te 5.

$$m=\frac{-\left(-2\right)±\sqrt{4-20}}{2}$$

Tāpiri 4 ki te -20.

$$m=\frac{-\left(-2\right)±\sqrt{-16}}{2}$$

Tuhia te pūtakerua o te -16.

$$m=\frac{-\left(-2\right)±4i}{2}$$

Ko te tauaro o -2 ko 2.

$$m=\frac{2±4i}{2}$$

Nā, me whakaoti te whārite m=\frac{2±4i}{2} ina he tāpiri te ±. Tāpiri 2 ki te 4i.

$$m=\frac{2+4i}{2}$$

Whakawehe 2+4i ki te 2.

$$m=1+2i$$

Nā, me whakaoti te whārite m=\frac{2±4i}{2} ina he tango te ±. Tango 4i mai i 2.

$$m=\frac{2-4i}{2}$$

Whakawehe 2-4i ki te 2.

$$m=1-2i$$

Kua oti te whārite te whakatau.

$$m=1+2i m=1-2i$$

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.

$$m^{2}-2m+5=0$$

Me tango 5 mai i ngā taha e rua o te whārite.

$$m^{2}-2m+5-5=-5$$

Mā te tango i te 5 i a ia ake anō ka toe ko te 0.

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

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.

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

Tāpiri -5 ki te 1.

$$m^{2}-2m+1=-4$$

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}.

$$\left(m-1\right)^{2}=-4$$

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

$$\sqrt{\left(m-1\right)^{2}}=\sqrt{-4}$$

Whakarūnātia.

$$m-1=2i m-1=-2i$$

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

$$m=1+2i m=1-2i$$