Whakaoti i te 3x^2-6x+1

$$3 { x }^{ 2 } -6x+1$$

Tauwehe

$$3\left(x-\left(-\frac{\sqrt{6}}{3}+1\right)\right)\left(x-\left(\frac{\sqrt{6}}{3}+1\right)\right)$$

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.

$$3x^{2}-6x+1=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 3}}{2\times 3}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 3}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-6\right)±\sqrt{36-12}}{2\times 3}$$

Tāpiri 36 ki te -12.

$$x=\frac{-\left(-6\right)±\sqrt{24}}{2\times 3}$$

Tuhia te pūtakerua o te 24.

$$x=\frac{-\left(-6\right)±2\sqrt{6}}{2\times 3}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±2\sqrt{6}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{6±2\sqrt{6}}{6}$$

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

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

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

$$x=\frac{\sqrt{6}}{3}+1$$

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

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

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

$$x=-\frac{\sqrt{6}}{3}+1$$

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+\frac{\sqrt{6}}{3} mō te x_{1} me te 1-\frac{\sqrt{6}}{3} mō te x_{2}.

$$3x^{2}-6x+1=3\left(x-\left(\frac{\sqrt{6}}{3}+1\right)\right)\left(x-\left(-\frac{\sqrt{6}}{3}+1\right)\right)$$

Aromātai

$$3x^{2}-6x+1$$