Whakaoti i te a^2-2a-30=0

$$a ^ { 2 } - 2 a - 30 = 0$$

Whakaoti mō a

$$a=\sqrt{31}+1\approx 6.567764363$$

$$a=1-\sqrt{31}\approx -4.567764363$$

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.

$$a^{2}-2a-30=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me -30 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-30\right)}}{2}$$

Pūrua -2.

$$a=\frac{-\left(-2\right)±\sqrt{4-4\left(-30\right)}}{2}$$

Whakareatia -4 ki te -30.

$$a=\frac{-\left(-2\right)±\sqrt{4+120}}{2}$$

Tāpiri 4 ki te 120.

$$a=\frac{-\left(-2\right)±\sqrt{124}}{2}$$

Tuhia te pūtakerua o te 124.

$$a=\frac{-\left(-2\right)±2\sqrt{31}}{2}$$

Ko te tauaro o -2 ko 2.

$$a=\frac{2±2\sqrt{31}}{2}$$

Nā, me whakaoti te whārite a=\frac{2±2\sqrt{31}}{2} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{31}.

$$a=\frac{2\sqrt{31}+2}{2}$$

Whakawehe 2+2\sqrt{31} ki te 2.

$$a=\sqrt{31}+1$$

Nā, me whakaoti te whārite a=\frac{2±2\sqrt{31}}{2} ina he tango te ±. Tango 2\sqrt{31} mai i 2.

$$a=\frac{2-2\sqrt{31}}{2}$$

Whakawehe 2-2\sqrt{31} ki te 2.

$$a=1-\sqrt{31}$$

Kua oti te whārite te whakatau.

$$a=\sqrt{31}+1 a=1-\sqrt{31}$$

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.

$$a^{2}-2a-30=0$$

Me tāpiri 30 ki ngā taha e rua o te whārite.

$$a^{2}-2a-30-\left(-30\right)=-\left(-30\right)$$

Mā te tango i te -30 i a ia ake anō ka toe ko te 0.

$$a^{2}-2a=-\left(-30\right)$$

Tango -30 mai i 0.

$$a^{2}-2a=30$$

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.

$$a^{2}-2a+1=30+1$$

Tāpiri 30 ki te 1.

$$a^{2}-2a+1=31$$

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}.

$$\left(a-1\right)^{2}=31$$

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

$$\sqrt{\left(a-1\right)^{2}}=\sqrt{31}$$

Whakarūnātia.

$$a-1=\sqrt{31} a-1=-\sqrt{31}$$

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

$$a=\sqrt{31}+1 a=1-\sqrt{31}$$