Whakaoti i te 12113x^2-x-10

$$12113 x ^ { 2 } - x - 10$$

Tauwehe

$$12113\left(x-\frac{1-\sqrt{484521}}{24226}\right)\left(x-\frac{\sqrt{484521}+1}{24226}\right)$$

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.

$$12113x^{2}-x-10=0$$

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.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 12113\left(-10\right)}}{2\times 12113}$$

Whakareatia -4 ki te 12113.

$$x=\frac{-\left(-1\right)±\sqrt{1-48452\left(-10\right)}}{2\times 12113}$$

Whakareatia -48452 ki te -10.

$$x=\frac{-\left(-1\right)±\sqrt{1+484520}}{2\times 12113}$$

Tāpiri 1 ki te 484520.

$$x=\frac{-\left(-1\right)±\sqrt{484521}}{2\times 12113}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±\sqrt{484521}}{2\times 12113}$$

Whakareatia 2 ki te 12113.

$$x=\frac{1±\sqrt{484521}}{24226}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{484521}}{24226} ina he tāpiri te ±. Tāpiri 1 ki te \sqrt{484521}.

$$x=\frac{\sqrt{484521}+1}{24226}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{484521}}{24226} ina he tango te ±. Tango \sqrt{484521} mai i 1.

$$x=\frac{1-\sqrt{484521}}{24226}$$

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{484521}}{24226} mō te x_{1} me te \frac{1-\sqrt{484521}}{24226} mō te x_{2}.

$$12113x^{2}-x-10=12113\left(x-\frac{\sqrt{484521}+1}{24226}\right)\left(x-\frac{1-\sqrt{484521}}{24226}\right)$$

Aromātai

$$12113x^{2}-x-10$$