Whakaoti i te 3x^2-9x+3

$$3 { x }^{ 2 } -9x+3$$

Tauwehe

$$3\left(x-\frac{3-\sqrt{5}}{2}\right)\left(x-\frac{\sqrt{5}+3}{2}\right)$$

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.

$$3x^{2}-9x+3=0$$

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.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 3\times 3}}{2\times 3}$$

Pūrua -9.

$$x=\frac{-\left(-9\right)±\sqrt{81-4\times 3\times 3}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-9\right)±\sqrt{81-12\times 3}}{2\times 3}$$

Whakareatia -12 ki te 3.

$$x=\frac{-\left(-9\right)±\sqrt{81-36}}{2\times 3}$$

Tāpiri 81 ki te -36.

$$x=\frac{-\left(-9\right)±\sqrt{45}}{2\times 3}$$

Tuhia te pūtakerua o te 45.

$$x=\frac{-\left(-9\right)±3\sqrt{5}}{2\times 3}$$

Ko te tauaro o -9 ko 9.

$$x=\frac{9±3\sqrt{5}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{9±3\sqrt{5}}{6}$$

Nā, me whakaoti te whārite x=\frac{9±3\sqrt{5}}{6} ina he tāpiri te ±. Tāpiri 9 ki te 3\sqrt{5}.

$$x=\frac{3\sqrt{5}+9}{6}$$

Whakawehe 9+3\sqrt{5} ki te 6.

$$x=\frac{\sqrt{5}+3}{2}$$

Nā, me whakaoti te whārite x=\frac{9±3\sqrt{5}}{6} ina he tango te ±. Tango 3\sqrt{5} mai i 9.

$$x=\frac{9-3\sqrt{5}}{6}$$

Whakawehe 9-3\sqrt{5} ki te 6.

$$x=\frac{3-\sqrt{5}}{2}$$

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{3+\sqrt{5}}{2} mō te x_{1} me te \frac{3-\sqrt{5}}{2} mō te x_{2}.

$$3x^{2}-9x+3=3\left(x-\frac{\sqrt{5}+3}{2}\right)\left(x-\frac{3-\sqrt{5}}{2}\right)$$

Aromātai

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