Whakaoti i te 2a-1=(a-2)(a+2)

$$2 a - 1 = ( a - 2 ) ( a + 2 )$$

Whakaoti mō a

$$a=-1$$

$$a=3$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakaarohia te \left(a-2\right)\left(a+2\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 2.

$$2a-1=a^{2}-4$$

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

$$2a-1-a^{2}=-4$$

Me tāpiri te 4 ki ngā taha e rua.

$$2a-1-a^{2}+4=0$$

Tāpirihia te -1 ki te 4, ka 3.

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

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.

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

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -1 mō a, 2 mō b, me 3 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-2±\sqrt{2^{2}-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Pūrua 2.

$$a=\frac{-2±\sqrt{4-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$a=\frac{-2±\sqrt{4+4\times 3}}{2\left(-1\right)}$$

Whakareatia 4 ki te 3.

$$a=\frac{-2±\sqrt{4+12}}{2\left(-1\right)}$$

Tāpiri 4 ki te 12.

$$a=\frac{-2±\sqrt{16}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 16.

$$a=\frac{-2±4}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$a=\frac{-2±4}{-2}$$

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

$$a=\frac{2}{-2}$$

Whakawehe 2 ki te -2.

$$a=-1$$

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

$$a=-\frac{6}{-2}$$

Whakawehe -6 ki te -2.

$$a=3$$

Kua oti te whārite te whakatau.

$$a=-1 a=3$$

Ngā Upane mō te Whakaoti i te Pūrua

Whakaarohia te \left(a-2\right)\left(a+2\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Pūrua 2.

$$2a-1=a^{2}-4$$

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

$$2a-1-a^{2}=-4$$

Me tāpiri te 1 ki ngā taha e rua.

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

Tāpirihia te -4 ki te 1, ka -3.

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

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.

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

Whakawehea ngā taha e rua ki te -1.

$$\frac{-a^{2}+2a}{-1}=-\frac{3}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$a^{2}+\frac{2}{-1}a=-\frac{3}{-1}$$

Whakawehe 2 ki te -1.

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

Whakawehe -3 ki te -1.

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

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.

$$a^{2}-2a+1=3+1$$

Tāpiri 3 ki te 1.

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

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

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

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

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

Whakarūnātia.

$$a-1=2 a-1=-2$$

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

$$a=3 a=-1$$