Whakaoti i te m^2+6m-6

$$m ^ { 2 } + 6 m - 6$$

Tauwehe

$$\left(m-\left(-\sqrt{15}-3\right)\right)\left(m-\left(\sqrt{15}-3\right)\right)$$

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.

$$m^{2}+6m-6=0$$

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.

$$m=\frac{-6±\sqrt{6^{2}-4\left(-6\right)}}{2}$$

Pūrua 6.

$$m=\frac{-6±\sqrt{36-4\left(-6\right)}}{2}$$

Whakareatia -4 ki te -6.

$$m=\frac{-6±\sqrt{36+24}}{2}$$

Tāpiri 36 ki te 24.

$$m=\frac{-6±\sqrt{60}}{2}$$

Tuhia te pūtakerua o te 60.

$$m=\frac{-6±2\sqrt{15}}{2}$$

Nā, me whakaoti te whārite m=\frac{-6±2\sqrt{15}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{15}.

$$m=\frac{2\sqrt{15}-6}{2}$$

Whakawehe -6+2\sqrt{15} ki te 2.

$$m=\sqrt{15}-3$$

Nā, me whakaoti te whārite m=\frac{-6±2\sqrt{15}}{2} ina he tango te ±. Tango 2\sqrt{15} mai i -6.

$$m=\frac{-2\sqrt{15}-6}{2}$$

Whakawehe -6-2\sqrt{15} ki te 2.

$$m=-\sqrt{15}-3$$

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{15} mō te x_{1} me te -3-\sqrt{15} mō te x_{2}.

$$m^{2}+6m-6=\left(m-\left(\sqrt{15}-3\right)\right)\left(m-\left(-\sqrt{15}-3\right)\right)$$

Aromātai

$$m^{2}+6m-6$$