Whakaoti i te a^2+2=a-4

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

Whakaoti mō a

$$a=\frac{1+\sqrt{23}i}{2}\approx 0.5+2.397915762i$$

$$a=\frac{-\sqrt{23}i+1}{2}\approx 0.5-2.397915762i$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tangohia te a mai i ngā taha e rua.

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

Me tāpiri te 4 ki ngā taha e rua.

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

Tāpirihia te 2 ki te 4, ka 6.

$$a^{2}+6-a=0$$

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.

$$a^{2}-a+6=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -1 mō b, me 6 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-\left(-1\right)±\sqrt{1-4\times 6}}{2}$$

Whakareatia -4 ki te 6.

$$a=\frac{-\left(-1\right)±\sqrt{1-24}}{2}$$

Tāpiri 1 ki te -24.

$$a=\frac{-\left(-1\right)±\sqrt{-23}}{2}$$

Tuhia te pūtakerua o te -23.

$$a=\frac{-\left(-1\right)±\sqrt{23}i}{2}$$

Ko te tauaro o -1 ko 1.

$$a=\frac{1±\sqrt{23}i}{2}$$

Nā, me whakaoti te whārite a=\frac{1±\sqrt{23}i}{2} ina he tāpiri te ±. Tāpiri 1 ki te i\sqrt{23}.

$$a=\frac{1+\sqrt{23}i}{2}$$

Nā, me whakaoti te whārite a=\frac{1±\sqrt{23}i}{2} ina he tango te ±. Tango i\sqrt{23} mai i 1.

$$a=\frac{-\sqrt{23}i+1}{2}$$

Kua oti te whārite te whakatau.

$$a=\frac{1+\sqrt{23}i}{2} a=\frac{-\sqrt{23}i+1}{2}$$

Ngā Upane mō te Whakaoti i te Pūrua

Tangohia te a mai i ngā taha e rua.

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

Tangohia te 2 mai i ngā taha e rua.

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

Tangohia te 2 i te -4, ka -6.

$$a^{2}-a=-6$$

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

$$a^{2}-a+\left(-\frac{1}{2}\right)^{2}=-6+\left(-\frac{1}{2}\right)^{2}$$

Pūruatia -\frac{1}{2} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$a^{2}-a+\frac{1}{4}=-6+\frac{1}{4}$$

Tāpiri -6 ki te \frac{1}{4}.

$$a^{2}-a+\frac{1}{4}=-\frac{23}{4}$$

Tauwehea a^{2}-a+\frac{1}{4}. 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}.

$$\left(a-\frac{1}{2}\right)^{2}=-\frac{23}{4}$$

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

$$\sqrt{\left(a-\frac{1}{2}\right)^{2}}=\sqrt{-\frac{23}{4}}$$

Whakarūnātia.

$$a-\frac{1}{2}=\frac{\sqrt{23}i}{2} a-\frac{1}{2}=-\frac{\sqrt{23}i}{2}$$

Me tāpiri \frac{1}{2} ki ngā taha e rua o te whārite.

$$a=\frac{1+\sqrt{23}i}{2} a=\frac{-\sqrt{23}i+1}{2}$$