Whakaoti i te (11n^2+2n-8)+(4n^2-5n+7)

$$( 11 n ^ { 2 } + 2 n - 8 ) + ( 4 n ^ { 2 } - 5 n + 7 )$$

Aromātai

$$15n^{2}-3n-1$$

Ngā Upane Otinga

Pahekotia te 11n^{2} me 4n^{2}, ka 15n^{2}.

$$15n^{2}+2n-8-5n+7$$

Pahekotia te 2n me -5n, ka -3n.

$$15n^{2}-3n-8+7$$

Tāpirihia te -8 ki te 7, ka -1.

$$15n^{2}-3n-1$$

Tauwehe

$$15\left(n-\left(-\frac{\sqrt{69}}{30}+\frac{1}{10}\right)\right)\left(n-\left(\frac{\sqrt{69}}{30}+\frac{1}{10}\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 11n^{2} me 4n^{2}, ka 15n^{2}.

$$factor(15n^{2}+2n-8-5n+7)$$

Pahekotia te 2n me -5n, ka -3n.

$$factor(15n^{2}-3n-8+7)$$

Tāpirihia te -8 ki te 7, ka -1.

$$factor(15n^{2}-3n-1)$$

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.

$$15n^{2}-3n-1=0$$

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.

$$n=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 15\left(-1\right)}}{2\times 15}$$

Pūrua -3.

$$n=\frac{-\left(-3\right)±\sqrt{9-4\times 15\left(-1\right)}}{2\times 15}$$

Whakareatia -4 ki te 15.

$$n=\frac{-\left(-3\right)±\sqrt{9-60\left(-1\right)}}{2\times 15}$$

Whakareatia -60 ki te -1.

$$n=\frac{-\left(-3\right)±\sqrt{9+60}}{2\times 15}$$

Tāpiri 9 ki te 60.

$$n=\frac{-\left(-3\right)±\sqrt{69}}{2\times 15}$$

Ko te tauaro o -3 ko 3.

$$n=\frac{3±\sqrt{69}}{2\times 15}$$

Whakareatia 2 ki te 15.

$$n=\frac{3±\sqrt{69}}{30}$$

Nā, me whakaoti te whārite n=\frac{3±\sqrt{69}}{30} ina he tāpiri te ±. Tāpiri 3 ki te \sqrt{69}.

$$n=\frac{\sqrt{69}+3}{30}$$

Whakawehe 3+\sqrt{69} ki te 30.

$$n=\frac{\sqrt{69}}{30}+\frac{1}{10}$$

Nā, me whakaoti te whārite n=\frac{3±\sqrt{69}}{30} ina he tango te ±. Tango \sqrt{69} mai i 3.

$$n=\frac{3-\sqrt{69}}{30}$$

Whakawehe 3-\sqrt{69} ki te 30.

$$n=-\frac{\sqrt{69}}{30}+\frac{1}{10}$$

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}{10}+\frac{\sqrt{69}}{30} mō te x_{1} me te \frac{1}{10}-\frac{\sqrt{69}}{30} mō te x_{2}.

$$15n^{2}-3n-1=15\left(n-\left(\frac{\sqrt{69}}{30}+\frac{1}{10}\right)\right)\left(n-\left(-\frac{\sqrt{69}}{30}+\frac{1}{10}\right)\right)$$