Whakaoti i te m^2-12m+10

$$m ^ { 2 } - 12 m + 10$$

Tauwehe

$$\left(m-\left(6-\sqrt{26}\right)\right)\left(m-\left(\sqrt{26}+6\right)\right)$$

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.

$$m^{2}-12m+10=0$$

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.

$$m=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 10}}{2}$$

Pūrua -12.

$$m=\frac{-\left(-12\right)±\sqrt{144-4\times 10}}{2}$$

Whakareatia -4 ki te 10.

$$m=\frac{-\left(-12\right)±\sqrt{144-40}}{2}$$

Tāpiri 144 ki te -40.

$$m=\frac{-\left(-12\right)±\sqrt{104}}{2}$$

Tuhia te pūtakerua o te 104.

$$m=\frac{-\left(-12\right)±2\sqrt{26}}{2}$$

Ko te tauaro o -12 ko 12.

$$m=\frac{12±2\sqrt{26}}{2}$$

Nā, me whakaoti te whārite m=\frac{12±2\sqrt{26}}{2} ina he tāpiri te ±. Tāpiri 12 ki te 2\sqrt{26}.

$$m=\frac{2\sqrt{26}+12}{2}$$

Whakawehe 12+2\sqrt{26} ki te 2.

$$m=\sqrt{26}+6$$

Nā, me whakaoti te whārite m=\frac{12±2\sqrt{26}}{2} ina he tango te ±. Tango 2\sqrt{26} mai i 12.

$$m=\frac{12-2\sqrt{26}}{2}$$

Whakawehe 12-2\sqrt{26} ki te 2.

$$m=6-\sqrt{26}$$

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 6+\sqrt{26} mō te x_{1} me te 6-\sqrt{26} mō te x_{2}.

$$m^{2}-12m+10=\left(m-\left(\sqrt{26}+6\right)\right)\left(m-\left(6-\sqrt{26}\right)\right)$$

Aromātai

$$m^{2}-12m+10$$