Whakaoti i te 3k^2-12k+9

$$3 k ^ { 2 } - 12 k + 9$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 3.

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

Whakaarohia te k^{2}-4k+3. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei k^{2}+ak+bk+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 k^{2}-4k+3 hei \left(k^{2}-3k\right)+\left(-k+3\right).

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

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

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

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.

$$3k^{2}-12k+9=0$$

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.

$$k=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 3\times 9}}{2\times 3}$$

Pūrua -12.

$$k=\frac{-\left(-12\right)±\sqrt{144-4\times 3\times 9}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$k=\frac{-\left(-12\right)±\sqrt{144-12\times 9}}{2\times 3}$$

Whakareatia -12 ki te 9.

$$k=\frac{-\left(-12\right)±\sqrt{144-108}}{2\times 3}$$

Tāpiri 144 ki te -108.

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

Tuhia te pūtakerua o te 36.

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

Ko te tauaro o -12 ko 12.

$$k=\frac{12±6}{2\times 3}$$

Whakareatia 2 ki te 3.

$$k=\frac{12±6}{6}$$

Nā, me whakaoti te whārite k=\frac{12±6}{6} ina he tāpiri te ±. Tāpiri 12 ki te 6.

$$k=\frac{18}{6}$$

Whakawehe 18 ki te 6.

$$k=3$$

Nā, me whakaoti te whārite k=\frac{12±6}{6} ina he tango te ±. Tango 6 mai i 12.

$$k=\frac{6}{6}$$

Whakawehe 6 ki te 6.

$$k=1$$

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}.

$$3k^{2}-12k+9=3\left(k-3\right)\left(k-1\right)$$

Aromātai

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