Whakaoti i te 72n^2-16n-8

$$72 { n }^{ 2 } -16n-8$$

Tauwehe

$$72\left(n-\frac{1-\sqrt{10}}{9}\right)\left(n-\frac{\sqrt{10}+1}{9}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$72n^{2}-16n-8=0$$

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.

$$n=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 72\left(-8\right)}}{2\times 72}$$

Pūrua -16.

$$n=\frac{-\left(-16\right)±\sqrt{256-4\times 72\left(-8\right)}}{2\times 72}$$

Whakareatia -4 ki te 72.

$$n=\frac{-\left(-16\right)±\sqrt{256-288\left(-8\right)}}{2\times 72}$$

Whakareatia -288 ki te -8.

$$n=\frac{-\left(-16\right)±\sqrt{256+2304}}{2\times 72}$$

Tāpiri 256 ki te 2304.

$$n=\frac{-\left(-16\right)±\sqrt{2560}}{2\times 72}$$

Tuhia te pūtakerua o te 2560.

$$n=\frac{-\left(-16\right)±16\sqrt{10}}{2\times 72}$$

Ko te tauaro o -16 ko 16.

$$n=\frac{16±16\sqrt{10}}{2\times 72}$$

Whakareatia 2 ki te 72.

$$n=\frac{16±16\sqrt{10}}{144}$$

Nā, me whakaoti te whārite n=\frac{16±16\sqrt{10}}{144} ina he tāpiri te ±. Tāpiri 16 ki te 16\sqrt{10}.

$$n=\frac{16\sqrt{10}+16}{144}$$

Whakawehe 16+16\sqrt{10} ki te 144.

$$n=\frac{\sqrt{10}+1}{9}$$

Nā, me whakaoti te whārite n=\frac{16±16\sqrt{10}}{144} ina he tango te ±. Tango 16\sqrt{10} mai i 16.

$$n=\frac{16-16\sqrt{10}}{144}$$

Whakawehe 16-16\sqrt{10} ki te 144.

$$n=\frac{1-\sqrt{10}}{9}$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te \frac{1+\sqrt{10}}{9} mō te x_{1} me te \frac{1-\sqrt{10}}{9} mō te x_{2}.

$$72n^{2}-16n-8=72\left(n-\frac{\sqrt{10}+1}{9}\right)\left(n-\frac{1-\sqrt{10}}{9}\right)$$

Aromātai

$$72n^{2}-16n-8$$