Whakaoti i te x^2-24x+2

$$x ^ { 2 } - 24 x + 2$$

Tauwehe

$$\left(x-\left(12-\sqrt{142}\right)\right)\left(x-\left(\sqrt{142}+12\right)\right)$$

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.

$$x^{2}-24x+2=0$$

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.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 2}}{2}$$

Pūrua -24.

$$x=\frac{-\left(-24\right)±\sqrt{576-4\times 2}}{2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-24\right)±\sqrt{576-8}}{2}$$

Tāpiri 576 ki te -8.

$$x=\frac{-\left(-24\right)±\sqrt{568}}{2}$$

Tuhia te pūtakerua o te 568.

$$x=\frac{-\left(-24\right)±2\sqrt{142}}{2}$$

Ko te tauaro o -24 ko 24.

$$x=\frac{24±2\sqrt{142}}{2}$$

Nā, me whakaoti te whārite x=\frac{24±2\sqrt{142}}{2} ina he tāpiri te ±. Tāpiri 24 ki te 2\sqrt{142}.

$$x=\frac{2\sqrt{142}+24}{2}$$

Whakawehe 24+2\sqrt{142} ki te 2.

$$x=\sqrt{142}+12$$

Nā, me whakaoti te whārite x=\frac{24±2\sqrt{142}}{2} ina he tango te ±. Tango 2\sqrt{142} mai i 24.

$$x=\frac{24-2\sqrt{142}}{2}$$

Whakawehe 24-2\sqrt{142} ki te 2.

$$x=12-\sqrt{142}$$

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 12+\sqrt{142} mō te x_{1} me te 12-\sqrt{142} mō te x_{2}.

$$x^{2}-24x+2=\left(x-\left(\sqrt{142}+12\right)\right)\left(x-\left(12-\sqrt{142}\right)\right)$$

Aromātai

$$x^{2}-24x+2$$