Whakaoti i te 6x^2-12x+6

$$6 x ^ { 2 } - 12 x + 6$$

Tauwehe

$$6\left(x-1\right)^{2}$$

Ngā Upane Otinga

Tauwehea te 6.

$$6\left(x^{2}-2x+1\right)$$

Whakaarohia te x^{2}-2x+1. Whakamahia te tikanga tātai pūrua pā, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, ina a=x, ina b=1.

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$6\left(x-1\right)^{2}$$

Ngā Upane Whakamahi Tauwehe o te Pūrua Huarua

Ko te tikanga tātai o tēnei huatoru he pūrua huatoru, ka whakareatia pea e tētahi tauwehe pātahi. Ka taea ngā pūrua huatoru te tauwehe mā te kimi i ngā pūtakerua o ngā kīanga tau ārahi, autō hoki.

$$factor(6x^{2}-12x+6)$$

Kimihia te tauwehe pātahi nui rawa o ngā tau whakarea.

$$gcf(6,-12,6)=6$$

Tauwehea te 6.

$$6\left(x^{2}-2x+1\right)$$

Ko te pūrua huatoru te pūrua o te huarua ko te tapeke tērā, te huatango rānei o ngā pūtakerua o ngā kīanga tau ārahi, autō hoki, e whakaritea ai te tohu e te tohu o te kīanga tau waenga o te pūrua huatoru.

$$6\left(x-1\right)^{2}$$

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.

$$6x^{2}-12x+6=0$$

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.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 6\times 6}}{2\times 6}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 6\times 6}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-\left(-12\right)±\sqrt{144-24\times 6}}{2\times 6}$$

Whakareatia -24 ki te 6.

$$x=\frac{-\left(-12\right)±\sqrt{144-144}}{2\times 6}$$

Tāpiri 144 ki te -144.

$$x=\frac{-\left(-12\right)±\sqrt{0}}{2\times 6}$$

Tuhia te pūtakerua o te 0.

$$x=\frac{-\left(-12\right)±0}{2\times 6}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±0}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{12±0}{12}$$

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 mō te x_{1} me te 1 mō te x_{2}.

$$6x^{2}-12x+6=6\left(x-1\right)\left(x-1\right)$$

Aromātai

$$6\left(x-1\right)^{2}$$