Whakaoti i te -x^2-6x+8

$$- x ^ { 2 } - 6 x + 8$$

Tauwehe

$$-\left(x-\left(-\sqrt{17}-3\right)\right)\left(x-\left(\sqrt{17}-3\right)\right)$$

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.

$$-x^{2}-6x+8=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-1\right)\times 8}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-6\right)±\sqrt{36+4\times 8}}{2\left(-1\right)}$$

Whakareatia 4 ki te 8.

$$x=\frac{-\left(-6\right)±\sqrt{36+32}}{2\left(-1\right)}$$

Tāpiri 36 ki te 32.

$$x=\frac{-\left(-6\right)±\sqrt{68}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 68.

$$x=\frac{-\left(-6\right)±2\sqrt{17}}{2\left(-1\right)}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±2\sqrt{17}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{6±2\sqrt{17}}{-2}$$

Nā, me whakaoti te whārite x=\frac{6±2\sqrt{17}}{-2} ina he tāpiri te ±. Tāpiri 6 ki te 2\sqrt{17}.

$$x=\frac{2\sqrt{17}+6}{-2}$$

Whakawehe 6+2\sqrt{17} ki te -2.

$$x=-\left(\sqrt{17}+3\right)$$

Nā, me whakaoti te whārite x=\frac{6±2\sqrt{17}}{-2} ina he tango te ±. Tango 2\sqrt{17} mai i 6.

$$x=\frac{6-2\sqrt{17}}{-2}$$

Whakawehe 6-2\sqrt{17} ki te -2.

$$x=\sqrt{17}-3$$

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 -\left(3+\sqrt{17}\right) mō te x_{1} me te -3+\sqrt{17} mō te x_{2}.

$$-x^{2}-6x+8=-\left(x-\left(-\left(\sqrt{17}+3\right)\right)\right)\left(x-\left(\sqrt{17}-3\right)\right)$$

Aromātai

$$8-6x-x^{2}$$