Whakaoti i te n^2+3n+3n+6

$$n ^ { 2 } + 3 n + 3 n + 6$$

Tauwehe

$$\left(n-\left(-\sqrt{3}-3\right)\right)\left(n-\left(\sqrt{3}-3\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 3n me 3n, ka 6n.

$$factor(n^{2}+6n+6)$$

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.

$$n^{2}+6n+6=0$$

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.

$$n=\frac{-6±\sqrt{6^{2}-4\times 6}}{2}$$

Pūrua 6.

$$n=\frac{-6±\sqrt{36-4\times 6}}{2}$$

Whakareatia -4 ki te 6.

$$n=\frac{-6±\sqrt{36-24}}{2}$$

Tāpiri 36 ki te -24.

$$n=\frac{-6±\sqrt{12}}{2}$$

Tuhia te pūtakerua o te 12.

$$n=\frac{-6±2\sqrt{3}}{2}$$

Nā, me whakaoti te whārite n=\frac{-6±2\sqrt{3}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{3}.

$$n=\frac{2\sqrt{3}-6}{2}$$

Whakawehe -6+2\sqrt{3} ki te 2.

$$n=\sqrt{3}-3$$

Nā, me whakaoti te whārite n=\frac{-6±2\sqrt{3}}{2} ina he tango te ±. Tango 2\sqrt{3} mai i -6.

$$n=\frac{-2\sqrt{3}-6}{2}$$

Whakawehe -6-2\sqrt{3} ki te 2.

$$n=-\sqrt{3}-3$$

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 -3+\sqrt{3} mō te x_{1} me te -3-\sqrt{3} mō te x_{2}.

$$n^{2}+6n+6=\left(n-\left(\sqrt{3}-3\right)\right)\left(n-\left(-\sqrt{3}-3\right)\right)$$

Aromātai

$$n^{2}+6n+6$$

Ngā Upane Otinga

Pahekotia te 3n me 3n, ka 6n.

$$n^{2}+6n+6$$