Whakaoti i te 2x^2-8x+6

$$2 x ^ { 2 } - 8 x + 6$$

Tauwehe

$$2\left(x-3\right)\left(x-1\right)$$

Ngā Upane Otinga

Tauwehea te 2.

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

Whakaarohia te x^{2}-4x+3. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-4 ab=1\times 3=3$$

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.

$$a=-3 b=-1$$

Tuhia anō te x^{2}-4x+3 hei \left(x^{2}-3x\right)+\left(-x+3\right).

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

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

$$x\left(x-3\right)-\left(x-3\right)$$

Whakatauwehea atu te kīanga pātahi x-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-3\right)\left(x-1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(x-3\right)\left(x-1\right)$$

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.

$$2x^{2}-8x+6=0$$

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.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 2\times 6}}{2\times 2}$$

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 2\times 6}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-8\right)±\sqrt{64-8\times 6}}{2\times 2}$$

Whakareatia -8 ki te 6.

$$x=\frac{-\left(-8\right)±\sqrt{64-48}}{2\times 2}$$

Tāpiri 64 ki te -48.

$$x=\frac{-\left(-8\right)±\sqrt{16}}{2\times 2}$$

Tuhia te pūtakerua o te 16.

$$x=\frac{-\left(-8\right)±4}{2\times 2}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8±4}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{8±4}{4}$$

Nā, me whakaoti te whārite x=\frac{8±4}{4} ina he tāpiri te ±. Tāpiri 8 ki te 4.

$$x=\frac{12}{4}$$

Whakawehe 12 ki te 4.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{8±4}{4} ina he tango te ±. Tango 4 mai i 8.

$$x=\frac{4}{4}$$

Whakawehe 4 ki te 4.

$$x=1$$

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 3 mō te x_{1} me te 1 mō te x_{2}.

$$2x^{2}-8x+6=2\left(x-3\right)\left(x-1\right)$$

Aromātai

$$2\left(x-3\right)\left(x-1\right)$$