Whakaoti i te x^2-16x-48

$$x ^ { 2 } - 16 x - 48$$

Tauwehe

$$\left(x-\left(8-4\sqrt{7}\right)\right)\left(x-\left(4\sqrt{7}+8\right)\right)$$

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.

$$x^{2}-16x-48=0$$

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.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\left(-48\right)}}{2}$$

Pūrua -16.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\left(-48\right)}}{2}$$

Whakareatia -4 ki te -48.

$$x=\frac{-\left(-16\right)±\sqrt{256+192}}{2}$$

Tāpiri 256 ki te 192.

$$x=\frac{-\left(-16\right)±\sqrt{448}}{2}$$

Tuhia te pūtakerua o te 448.

$$x=\frac{-\left(-16\right)±8\sqrt{7}}{2}$$

Ko te tauaro o -16 ko 16.

$$x=\frac{16±8\sqrt{7}}{2}$$

Nā, me whakaoti te whārite x=\frac{16±8\sqrt{7}}{2} ina he tāpiri te ±. Tāpiri 16 ki te 8\sqrt{7}.

$$x=\frac{8\sqrt{7}+16}{2}$$

Whakawehe 16+8\sqrt{7} ki te 2.

$$x=4\sqrt{7}+8$$

Nā, me whakaoti te whārite x=\frac{16±8\sqrt{7}}{2} ina he tango te ±. Tango 8\sqrt{7} mai i 16.

$$x=\frac{16-8\sqrt{7}}{2}$$

Whakawehe 16-8\sqrt{7} ki te 2.

$$x=8-4\sqrt{7}$$

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 8+4\sqrt{7} mō te x_{1} me te 8-4\sqrt{7} mō te x_{2}.

$$x^{2}-16x-48=\left(x-\left(4\sqrt{7}+8\right)\right)\left(x-\left(8-4\sqrt{7}\right)\right)$$

Aromātai

$$x^{2}-16x-48$$