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a+b=-2 ab=1\left(-3\right)=-3
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
a=-3 b=1
I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Ko te takirua anake pērā ko te otinga pūnaha.
\left(x^{2}-3x\right)+\left(x-3\right)
Tuhia anō te x^{2}-2x-3 hei \left(x^{2}-3x\right)+\left(x-3\right).
x\left(x-3\right)+x-3
Whakatauwehea atu x i te x^{2}-3x.
\left(x-3\right)\left(x+1\right)
Whakatauwehea atu te kīanga pātahi x-3 mā te whakamahi i te āhuatanga tātai tohatoha.
x^{2}-2x-3=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{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-3\right)}}{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{-\left(-2\right)±\sqrt{4-4\left(-3\right)}}{2}
Pūrua -2.
x=\frac{-\left(-2\right)±\sqrt{4+12}}{2}
Whakareatia -4 ki te -3.
x=\frac{-\left(-2\right)±\sqrt{16}}{2}
Tāpiri 4 ki te 12.
x=\frac{-\left(-2\right)±4}{2}
Tuhia te pūtakerua o te 16.
x=\frac{2±4}{2}
Ko te tauaro o -2 ko 2.
x=\frac{6}{2}
Nā, me whakaoti te whārite x=\frac{2±4}{2} ina he tāpiri te ±. Tāpiri 2 ki te 4.
x=3
Whakawehe 6 ki te 2.
x=-\frac{2}{2}
Nā, me whakaoti te whārite x=\frac{2±4}{2} ina he tango te ±. Tango 4 mai i 2.
x=-1
Whakawehe -2 ki te 2.
x^{2}-2x-3=\left(x-3\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 3 mō te x_{1} me te -1 mō te x_{2}.
x^{2}-2x-3=\left(x-3\right)\left(x+1\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.