Whakaoti i te 48-24x+3x^2

$$48-24x+3 { x }^{ 2 }$$

Tauwehe

$$3\left(x-4\right)^{2}$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(16-8x+x^{2}\right)$$

Whakaarohia te 16-8x+x^{2}. Whakamahia te tikanga tātai pūrua pā, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, ina a=x, ina b=4.

$$\left(x-4\right)^{2}$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3\left(x-4\right)^{2}$$

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.

$$factor(3x^{2}-24x+48)$$

Kimihia te tauwehe pātahi nui rawa o ngā tau whakarea.

$$gcf(3,-24,48)=3$$

Tauwehea te 3.

$$3\left(x^{2}-8x+16\right)$$

Kimihia te pūtakerua o te kīanga tau autō, 16.

$$\sqrt{16}=4$$

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.

$$3\left(x-4\right)^{2}$$

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.

$$3x^{2}-24x+48=0$$

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.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 3\times 48}}{2\times 3}$$

Pūrua -24.

$$x=\frac{-\left(-24\right)±\sqrt{576-4\times 3\times 48}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-24\right)±\sqrt{576-12\times 48}}{2\times 3}$$

Whakareatia -12 ki te 48.

$$x=\frac{-\left(-24\right)±\sqrt{576-576}}{2\times 3}$$

Tāpiri 576 ki te -576.

$$x=\frac{-\left(-24\right)±\sqrt{0}}{2\times 3}$$

Tuhia te pūtakerua o te 0.

$$x=\frac{-\left(-24\right)±0}{2\times 3}$$

Ko te tauaro o -24 ko 24.

$$x=\frac{24±0}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{24±0}{6}$$

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 4 mō te x_{1} me te 4 mō te x_{2}.

$$3x^{2}-24x+48=3\left(x-4\right)\left(x-4\right)$$

Aromātai

$$3\left(x-4\right)^{2}$$