Whakaoti i te f^2+16f+64

$$f ^ { 2 } + 16 f + 64$$

Tauwehe

$$\left(f+8\right)^{2}$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei f^{2}+af+bf+64. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=16 ab=1\times 64=64$$

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 64.

$$1,64 2,32 4,16 8,8$$

Tātaihia te tapeke mō ia takirua.

$$1+64=65 2+32=34 4+16=20 8+8=16$$

Ko te otinga te takirua ka hoatu i te tapeke 16.

$$a=8 b=8$$

Tuhia anō te f^{2}+16f+64 hei \left(f^{2}+8f\right)+\left(8f+64\right).

$$\left(f^{2}+8f\right)+\left(8f+64\right)$$

Tauwehea te f i te tuatahi me te 8 i te rōpū tuarua.

$$f\left(f+8\right)+8\left(f+8\right)$$

Whakatauwehea atu te kīanga pātahi f+8 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(f+8\right)\left(f+8\right)$$

Tuhia anōtia hei pūrua huarua.

$$\left(f+8\right)^{2}$$

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.

$$factor(f^{2}+16f+64)$$

Kimihia te pūtakerua o te kīanga tau autō, 64.

$$\sqrt{64}=8$$

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.

$$\left(f+8\right)^{2}$$

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.

$$f^{2}+16f+64=0$$

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.

$$f=\frac{-16±\sqrt{16^{2}-4\times 64}}{2}$$

Pūrua 16.

$$f=\frac{-16±\sqrt{256-4\times 64}}{2}$$

Whakareatia -4 ki te 64.

$$f=\frac{-16±\sqrt{256-256}}{2}$$

Tāpiri 256 ki te -256.

$$f=\frac{-16±\sqrt{0}}{2}$$

Tuhia te pūtakerua o te 0.

$$f=\frac{-16±0}{2}$$

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 -8 mō te x_{1} me te -8 mō te x_{2}.

$$f^{2}+16f+64=\left(f-\left(-8\right)\right)\left(f-\left(-8\right)\right)$$

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

$$f^{2}+16f+64=\left(f+8\right)\left(f+8\right)$$

Aromātai

$$\left(f+8\right)^{2}$$