Whakaoti i te 24x^2-72x+48

$$24 x ^ { 2 } - 72 x + 48$$

Tauwehe

$$24\left(x-2\right)\left(x-1\right)$$

Ngā Upane Otinga

Tauwehea te 24.

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

Whakaarohia te x^{2}-3x+2. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-3 ab=1\times 2=2$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-2 b=-1$$

Tuhia anō te x^{2}-3x+2 hei \left(x^{2}-2x\right)+\left(-x+2\right).

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

Tauwehea te x i te tuatahi me te -1 i te rōpū tuarua.

$$x\left(x-2\right)-\left(x-2\right)$$

Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-2\right)\left(x-1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$24\left(x-2\right)\left(x-1\right)$$

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.

$$24x^{2}-72x+48=0$$

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.

$$x=\frac{-\left(-72\right)±\sqrt{\left(-72\right)^{2}-4\times 24\times 48}}{2\times 24}$$

Pūrua -72.

$$x=\frac{-\left(-72\right)±\sqrt{5184-4\times 24\times 48}}{2\times 24}$$

Whakareatia -4 ki te 24.

$$x=\frac{-\left(-72\right)±\sqrt{5184-96\times 48}}{2\times 24}$$

Whakareatia -96 ki te 48.

$$x=\frac{-\left(-72\right)±\sqrt{5184-4608}}{2\times 24}$$

Tāpiri 5184 ki te -4608.

$$x=\frac{-\left(-72\right)±\sqrt{576}}{2\times 24}$$

Tuhia te pūtakerua o te 576.

$$x=\frac{-\left(-72\right)±24}{2\times 24}$$

Ko te tauaro o -72 ko 72.

$$x=\frac{72±24}{2\times 24}$$

Whakareatia 2 ki te 24.

$$x=\frac{72±24}{48}$$

Nā, me whakaoti te whārite x=\frac{72±24}{48} ina he tāpiri te ±. Tāpiri 72 ki te 24.

$$x=\frac{96}{48}$$

Whakawehe 96 ki te 48.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{72±24}{48} ina he tango te ±. Tango 24 mai i 72.

$$x=\frac{48}{48}$$

Whakawehe 48 ki te 48.

$$x=1$$

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 2 mō te x_{1} me te 1 mō te x_{2}.

$$24x^{2}-72x+48=24\left(x-2\right)\left(x-1\right)$$

Aromātai

$$24\left(x-2\right)\left(x-1\right)$$