Whakaoti i te x^2+32x+1

$$x ^ { 2 } + 32 x + 1$$

Tauwehe

$$\left(x-\left(-\sqrt{255}-16\right)\right)\left(x-\left(\sqrt{255}-16\right)\right)$$

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.

$$x^{2}+32x+1=0$$

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.

$$x=\frac{-32±\sqrt{32^{2}-4}}{2}$$

Pūrua 32.

$$x=\frac{-32±\sqrt{1024-4}}{2}$$

Tāpiri 1024 ki te -4.

$$x=\frac{-32±\sqrt{1020}}{2}$$

Tuhia te pūtakerua o te 1020.

$$x=\frac{-32±2\sqrt{255}}{2}$$

Nā, me whakaoti te whārite x=\frac{-32±2\sqrt{255}}{2} ina he tāpiri te ±. Tāpiri -32 ki te 2\sqrt{255}.

$$x=\frac{2\sqrt{255}-32}{2}$$

Whakawehe -32+2\sqrt{255} ki te 2.

$$x=\sqrt{255}-16$$

Nā, me whakaoti te whārite x=\frac{-32±2\sqrt{255}}{2} ina he tango te ±. Tango 2\sqrt{255} mai i -32.

$$x=\frac{-2\sqrt{255}-32}{2}$$

Whakawehe -32-2\sqrt{255} ki te 2.

$$x=-\sqrt{255}-16$$

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 -16+\sqrt{255} mō te x_{1} me te -16-\sqrt{255} mō te x_{2}.

$$x^{2}+32x+1=\left(x-\left(\sqrt{255}-16\right)\right)\left(x-\left(-\sqrt{255}-16\right)\right)$$

Aromātai

$$x^{2}+32x+1$$