Whakaoti i te 4n^2-n-812

$$4 n ^ { 2 } - n - 812$$

Tauwehe

$$4\left(n-\frac{1-\sqrt{12993}}{8}\right)\left(n-\frac{\sqrt{12993}+1}{8}\right)$$

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.

$$4n^{2}-n-812=0$$

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.

$$n=\frac{-\left(-1\right)±\sqrt{1-4\times 4\left(-812\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$n=\frac{-\left(-1\right)±\sqrt{1-16\left(-812\right)}}{2\times 4}$$

Whakareatia -16 ki te -812.

$$n=\frac{-\left(-1\right)±\sqrt{1+12992}}{2\times 4}$$

Tāpiri 1 ki te 12992.

$$n=\frac{-\left(-1\right)±\sqrt{12993}}{2\times 4}$$

Ko te tauaro o -1 ko 1.

$$n=\frac{1±\sqrt{12993}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$n=\frac{1±\sqrt{12993}}{8}$$

Nā, me whakaoti te whārite n=\frac{1±\sqrt{12993}}{8} ina he tāpiri te ±. Tāpiri 1 ki te \sqrt{12993}.

$$n=\frac{\sqrt{12993}+1}{8}$$

Nā, me whakaoti te whārite n=\frac{1±\sqrt{12993}}{8} ina he tango te ±. Tango \sqrt{12993} mai i 1.

$$n=\frac{1-\sqrt{12993}}{8}$$

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{12993}}{8} mō te x_{1} me te \frac{1-\sqrt{12993}}{8} mō te x_{2}.

$$4n^{2}-n-812=4\left(n-\frac{\sqrt{12993}+1}{8}\right)\left(n-\frac{1-\sqrt{12993}}{8}\right)$$

Aromātai

$$4n^{2}-n-812$$