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a+b=2 ab=1\times 1=1
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
a=1 b=1
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. Ko te takirua anake pērā ko te otinga pūnaha.
\left(x^{2}+x\right)+\left(x+1\right)
Tuhia anō te x^{2}+2x+1 hei \left(x^{2}+x\right)+\left(x+1\right).
x\left(x+1\right)+x+1
Whakatauwehea atu x i te x^{2}+x.
\left(x+1\right)\left(x+1\right)
Whakatauwehea atu te kīanga pātahi x+1 mā te whakamahi i te āhuatanga tātai tohatoha.
\left(x+1\right)^{2}
Tuhia anōtia hei pūrua huarua.
factor(x^{2}+2x+1)
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.
\left(x+1\right)^{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.
x^{2}+2x+1=0
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.
x=\frac{-2±\sqrt{2^{2}-4}}{2}
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.
x=\frac{-2±\sqrt{4-4}}{2}
Pūrua 2.
x=\frac{-2±\sqrt{0}}{2}
Tāpiri 4 ki te -4.
x=\frac{-2±0}{2}
Tuhia te pūtakerua o te 0.
x^{2}+2x+1=\left(x-\left(-1\right)\right)\left(x-\left(-1\right)\right)
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 -1 mō te x_{1} me te -1 mō te x_{2}.
x^{2}+2x+1=\left(x+1\right)\left(x+1\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.