Whakaoti i te n^2-2n-81=0

$$n ^ { 2 } - 2 n - 81 = 0$$

Whakaoti mō n

$$n=\sqrt{82}+1\approx 10.055385138$$

$$n=1-\sqrt{82}\approx -8.055385138$$

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.

$$n^{2}-2n-81=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi 1 mō a, -2 mō b, me -81 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-81\right)}}{2}$$

Pūrua -2.

$$n=\frac{-\left(-2\right)±\sqrt{4-4\left(-81\right)}}{2}$$

Whakareatia -4 ki te -81.

$$n=\frac{-\left(-2\right)±\sqrt{4+324}}{2}$$

Tāpiri 4 ki te 324.

$$n=\frac{-\left(-2\right)±\sqrt{328}}{2}$$

Tuhia te pūtakerua o te 328.

$$n=\frac{-\left(-2\right)±2\sqrt{82}}{2}$$

Ko te tauaro o -2 ko 2.

$$n=\frac{2±2\sqrt{82}}{2}$$

Nā, me whakaoti te whārite n=\frac{2±2\sqrt{82}}{2} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{82}.

$$n=\frac{2\sqrt{82}+2}{2}$$

Whakawehe 2+2\sqrt{82} ki te 2.

$$n=\sqrt{82}+1$$

Nā, me whakaoti te whārite n=\frac{2±2\sqrt{82}}{2} ina he tango te ±. Tango 2\sqrt{82} mai i 2.

$$n=\frac{2-2\sqrt{82}}{2}$$

Whakawehe 2-2\sqrt{82} ki te 2.

$$n=1-\sqrt{82}$$

Kua oti te whārite te whakatau.

$$n=\sqrt{82}+1 n=1-\sqrt{82}$$

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.

$$n^{2}-2n-81=0$$

Me tāpiri 81 ki ngā taha e rua o te whārite.

$$n^{2}-2n-81-\left(-81\right)=-\left(-81\right)$$

Mā te tango i te -81 i a ia ake anō ka toe ko te 0.

$$n^{2}-2n=-\left(-81\right)$$

Tango -81 mai i 0.

$$n^{2}-2n=81$$

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.

$$n^{2}-2n+1=81+1$$

Tāpiri 81 ki te 1.

$$n^{2}-2n+1=82$$

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

$$\left(n-1\right)^{2}=82$$

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

$$\sqrt{\left(n-1\right)^{2}}=\sqrt{82}$$

Whakarūnātia.

$$n-1=\sqrt{82} n-1=-\sqrt{82}$$

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

$$n=\sqrt{82}+1 n=1-\sqrt{82}$$