Whakaoti i te x^2-8x+15div3-x

$${ x }^{ 2 } -8x+15 \div 3-x$$

Aromātai

$$x^{2}-9x+5$$

Ngā Upane Otinga

Whakawehea te 15 ki te 3, kia riro ko 5.

$$x^{2}-8x+5-x$$

Pahekotia te -8x me -x, ka -9x.

$$x^{2}-9x+5$$

Tauwehe

$$\left(x-\frac{9-\sqrt{61}}{2}\right)\left(x-\frac{\sqrt{61}+9}{2}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea te 15 ki te 3, kia riro ko 5.

$$factor(x^{2}-8x+5-x)$$

Pahekotia te -8x me -x, ka -9x.

$$factor(x^{2}-9x+5)$$

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.

$$x^{2}-9x+5=0$$

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.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 5}}{2}$$

Pūrua -9.

$$x=\frac{-\left(-9\right)±\sqrt{81-4\times 5}}{2}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-9\right)±\sqrt{81-20}}{2}$$

Tāpiri 81 ki te -20.

$$x=\frac{-\left(-9\right)±\sqrt{61}}{2}$$

Ko te tauaro o -9 ko 9.

$$x=\frac{9±\sqrt{61}}{2}$$

Nā, me whakaoti te whārite x=\frac{9±\sqrt{61}}{2} ina he tāpiri te ±. Tāpiri 9 ki te \sqrt{61}.

$$x=\frac{\sqrt{61}+9}{2}$$

Nā, me whakaoti te whārite x=\frac{9±\sqrt{61}}{2} ina he tango te ±. Tango \sqrt{61} mai i 9.

$$x=\frac{9-\sqrt{61}}{2}$$

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 \frac{9+\sqrt{61}}{2} mō te x_{1} me te \frac{9-\sqrt{61}}{2} mō te x_{2}.

$$x^{2}-9x+5=\left(x-\frac{\sqrt{61}+9}{2}\right)\left(x-\frac{9-\sqrt{61}}{2}\right)$$