Whakaoti i te c^2-12c+27

$$c ^ { 2 } - 12 c + 27$$

Tauwehe

$$\left(c-9\right)\left(c-3\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei c^{2}+ac+bc+27. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-12 ab=1\times 27=27$$

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. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 27.

$$-1,-27 -3,-9$$

Tātaihia te tapeke mō ia takirua.

$$-1-27=-28 -3-9=-12$$

Ko te otinga te takirua ka hoatu i te tapeke -12.

$$a=-9 b=-3$$

Tuhia anō te c^{2}-12c+27 hei \left(c^{2}-9c\right)+\left(-3c+27\right).

$$\left(c^{2}-9c\right)+\left(-3c+27\right)$$

Tauwehea te c i te tuatahi me te -3 i te rōpū tuarua.

$$c\left(c-9\right)-3\left(c-9\right)$$

Whakatauwehea atu te kīanga pātahi c-9 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(c-9\right)\left(c-3\right)$$

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.

$$c^{2}-12c+27=0$$

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.

$$c=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 27}}{2}$$

Pūrua -12.

$$c=\frac{-\left(-12\right)±\sqrt{144-4\times 27}}{2}$$

Whakareatia -4 ki te 27.

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

Tāpiri 144 ki te -108.

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

Tuhia te pūtakerua o te 36.

$$c=\frac{-\left(-12\right)±6}{2}$$

Ko te tauaro o -12 ko 12.

$$c=\frac{12±6}{2}$$

Nā, me whakaoti te whārite c=\frac{12±6}{2} ina he tāpiri te ±. Tāpiri 12 ki te 6.

$$c=\frac{18}{2}$$

Whakawehe 18 ki te 2.

$$c=9$$

Nā, me whakaoti te whārite c=\frac{12±6}{2} ina he tango te ±. Tango 6 mai i 12.

$$c=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$c=3$$

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 9 mō te x_{1} me te 3 mō te x_{2}.

$$c^{2}-12c+27=\left(c-9\right)\left(c-3\right)$$

Aromātai

$$\left(c-9\right)\left(c-3\right)$$