Whakaoti i te t^2-4t+4

$$t ^ { 2 } - 4 t + 4$$

Tauwehe

$$\left(t-2\right)^{2}$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei t^{2}+at+bt+4. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

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

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 4.

$$-1,-4 -2,-2$$

Tātaihia te tapeke mō ia takirua.

$$-1-4=-5 -2-2=-4$$

Ko te otinga te takirua ka hoatu i te tapeke -4.

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

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

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

Tauwehea te t i te tuatahi me te -2 i te rōpū tuarua.

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

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

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

Tuhia anōtia hei pūrua huarua.

$$\left(t-2\right)^{2}$$

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.

$$factor(t^{2}-4t+4)$$

Kimihia te pūtakerua o te kīanga tau autō, 4.

$$\sqrt{4}=2$$

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.

$$\left(t-2\right)^{2}$$

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.

$$t^{2}-4t+4=0$$

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.

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

Pūrua -4.

$$t=\frac{-\left(-4\right)±\sqrt{16-4\times 4}}{2}$$

Whakareatia -4 ki te 4.

$$t=\frac{-\left(-4\right)±\sqrt{16-16}}{2}$$

Tāpiri 16 ki te -16.

$$t=\frac{-\left(-4\right)±\sqrt{0}}{2}$$

Tuhia te pūtakerua o te 0.

$$t=\frac{-\left(-4\right)±0}{2}$$

Ko te tauaro o -4 ko 4.

$$t=\frac{4±0}{2}$$

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 2 mō te x_{2}.

$$t^{2}-4t+4=\left(t-2\right)\left(t-2\right)$$

Aromātai

$$\left(t-2\right)^{2}$$