Whakaoti i te n^2+10n+25

$$n ^ { 2 } + 10 n + 25$$

Tauwehe

$$\left(n+5\right)^{2}$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei n^{2}+an+bn+25. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=10 ab=1\times 25=25$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. 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.

$$a=5 b=5$$

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

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

Tauwehea te n i te tuatahi me te 5 i te rōpū tuarua.

$$n\left(n+5\right)+5\left(n+5\right)$$

Whakatauwehea atu te kīanga pātahi n+5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(n+5\right)\left(n+5\right)$$

Tuhia anōtia hei pūrua huarua.

$$\left(n+5\right)^{2}$$

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.

$$factor(n^{2}+10n+25)$$

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.

$$\left(n+5\right)^{2}$$

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.

$$n^{2}+10n+25=0$$

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.

$$n=\frac{-10±\sqrt{10^{2}-4\times 25}}{2}$$

Pūrua 10.

$$n=\frac{-10±\sqrt{100-4\times 25}}{2}$$

Whakareatia -4 ki te 25.

$$n=\frac{-10±\sqrt{100-100}}{2}$$

Tāpiri 100 ki te -100.

$$n=\frac{-10±\sqrt{0}}{2}$$

Tuhia te pūtakerua o te 0.

$$n=\frac{-10±0}{2}$$

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}.

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

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

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

Aromātai

$$\left(n+5\right)^{2}$$