Whakaoti i te -x^2+2x+2

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

Tauwehe

$$-\left(x-\left(1-\sqrt{3}\right)\right)\left(x-\left(\sqrt{3}+1\right)\right)$$

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.

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

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.

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

Pūrua 2.

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

Whakareatia -4 ki te -1.

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

Whakareatia 4 ki te 2.

$$x=\frac{-2±\sqrt{4+8}}{2\left(-1\right)}$$

Tāpiri 4 ki te 8.

$$x=\frac{-2±\sqrt{12}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 12.

$$x=\frac{-2±2\sqrt{3}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-2±2\sqrt{3}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{3}}{-2} ina he tāpiri te ±. Tāpiri -2 ki te 2\sqrt{3}.

$$x=\frac{2\sqrt{3}-2}{-2}$$

Whakawehe -2+2\sqrt{3} ki te -2.

$$x=1-\sqrt{3}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{3}}{-2} ina he tango te ±. Tango 2\sqrt{3} mai i -2.

$$x=\frac{-2\sqrt{3}-2}{-2}$$

Whakawehe -2-2\sqrt{3} ki te -2.

$$x=\sqrt{3}+1$$

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 1-\sqrt{3} mō te x_{1} me te 1+\sqrt{3} mō te x_{2}.

$$-x^{2}+2x+2=-\left(x-\left(1-\sqrt{3}\right)\right)\left(x-\left(\sqrt{3}+1\right)\right)$$

Aromātai

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