Whakaoti i te x^2-16x-82

$${ x }^{ 2 } -16x-82$$

Tauwehe

$$\left(x-\left(8-\sqrt{146}\right)\right)\left(x-\left(\sqrt{146}+8\right)\right)$$

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.

$$x^{2}-16x-82=0$$

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.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\left(-82\right)}}{2}$$

Pūrua -16.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\left(-82\right)}}{2}$$

Whakareatia -4 ki te -82.

$$x=\frac{-\left(-16\right)±\sqrt{256+328}}{2}$$

Tāpiri 256 ki te 328.

$$x=\frac{-\left(-16\right)±\sqrt{584}}{2}$$

Tuhia te pūtakerua o te 584.

$$x=\frac{-\left(-16\right)±2\sqrt{146}}{2}$$

Ko te tauaro o -16 ko 16.

$$x=\frac{16±2\sqrt{146}}{2}$$

Nā, me whakaoti te whārite x=\frac{16±2\sqrt{146}}{2} ina he tāpiri te ±. Tāpiri 16 ki te 2\sqrt{146}.

$$x=\frac{2\sqrt{146}+16}{2}$$

Whakawehe 16+2\sqrt{146} ki te 2.

$$x=\sqrt{146}+8$$

Nā, me whakaoti te whārite x=\frac{16±2\sqrt{146}}{2} ina he tango te ±. Tango 2\sqrt{146} mai i 16.

$$x=\frac{16-2\sqrt{146}}{2}$$

Whakawehe 16-2\sqrt{146} ki te 2.

$$x=8-\sqrt{146}$$

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+\sqrt{146} mō te x_{1} me te 8-\sqrt{146} mō te x_{2}.

$$x^{2}-16x-82=\left(x-\left(\sqrt{146}+8\right)\right)\left(x-\left(8-\sqrt{146}\right)\right)$$

Aromātai

$$x^{2}-16x-82$$