Whakaoti i te a^2-10a+25

$$a ^ { 2 } - 10 a + 25$$

Tauwehe

$$\left(a-5\right)^{2}$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei a^{2}+pa+qa+25. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=-10 pq=1\times 25=25$$

I te mea kua tōrunga te pq, he ōrite te tohu o p me q. I te mea kua tōraro te p+q, he tōraro hoki a p me q. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 25.

$$-1,-25 -5,-5$$

Tātaihia te tapeke mō ia takirua.

$$-1-25=-26 -5-5=-10$$

Ko te otinga te takirua ka hoatu i te tapeke -10.

$$p=-5 q=-5$$

Tuhia anō te a^{2}-10a+25 hei \left(a^{2}-5a\right)+\left(-5a+25\right).

$$\left(a^{2}-5a\right)+\left(-5a+25\right)$$

Tauwehea te a i te tuatahi me te -5 i te rōpū tuarua.

$$a\left(a-5\right)-5\left(a-5\right)$$

Whakatauwehea atu te kīanga pātahi a-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(a-5\right)\left(a-5\right)$$

Tuhia anōtia hei pūrua huarua.

$$\left(a-5\right)^{2}$$

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.

$$factor(a^{2}-10a+25)$$

Kimihia te pūtakerua o te kīanga tau autō, 25.

$$\sqrt{25}=5$$

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.

$$\left(a-5\right)^{2}$$

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.

$$a^{2}-10a+25=0$$

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.

$$a=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 25}}{2}$$

Pūrua -10.

$$a=\frac{-\left(-10\right)±\sqrt{100-4\times 25}}{2}$$

Whakareatia -4 ki te 25.

$$a=\frac{-\left(-10\right)±\sqrt{100-100}}{2}$$

Tāpiri 100 ki te -100.

$$a=\frac{-\left(-10\right)±\sqrt{0}}{2}$$

Tuhia te pūtakerua o te 0.

$$a=\frac{-\left(-10\right)±0}{2}$$

Ko te tauaro o -10 ko 10.

$$a=\frac{10±0}{2}$$

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 5 mō te x_{1} me te 5 mō te x_{2}.

$$a^{2}-10a+25=\left(a-5\right)\left(a-5\right)$$

Aromātai

$$\left(a-5\right)^{2}$$