Tauwehe
\left(n+4\right)\left(n+9\right)
Aromātai
\left(n+4\right)\left(n+9\right)
Tohaina
Kua tāruatia ki te papatopenga
a+b=13 ab=1\times 36=36
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei n^{2}+an+bn+36. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,36 2,18 3,12 4,9 6,6
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 36.
1+36=37 2+18=20 3+12=15 4+9=13 6+6=12
Tātaihia te tapeke mō ia takirua.
a=4 b=9
Ko te otinga te takirua ka hoatu i te tapeke 13.
\left(n^{2}+4n\right)+\left(9n+36\right)
Tuhia anō te n^{2}+13n+36 hei \left(n^{2}+4n\right)+\left(9n+36\right).
n\left(n+4\right)+9\left(n+4\right)
Tauwehea te n i te tuatahi me te 9 i te rōpū tuarua.
\left(n+4\right)\left(n+9\right)
Whakatauwehea atu te kīanga pātahi n+4 mā te whakamahi i te āhuatanga tātai tohatoha.
n^{2}+13n+36=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.
n=\frac{-13±\sqrt{13^{2}-4\times 36}}{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.
n=\frac{-13±\sqrt{169-4\times 36}}{2}
Pūrua 13.
n=\frac{-13±\sqrt{169-144}}{2}
Whakareatia -4 ki te 36.
n=\frac{-13±\sqrt{25}}{2}
Tāpiri 169 ki te -144.
n=\frac{-13±5}{2}
Tuhia te pūtakerua o te 25.
n=-\frac{8}{2}
Nā, me whakaoti te whārite n=\frac{-13±5}{2} ina he tāpiri te ±. Tāpiri -13 ki te 5.
n=-4
Whakawehe -8 ki te 2.
n=-\frac{18}{2}
Nā, me whakaoti te whārite n=\frac{-13±5}{2} ina he tango te ±. Tango 5 mai i -13.
n=-9
Whakawehe -18 ki te 2.
n^{2}+13n+36=\left(n-\left(-4\right)\right)\left(n-\left(-9\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 -4 mō te x_{1} me te -9 mō te x_{2}.
n^{2}+13n+36=\left(n+4\right)\left(n+9\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.
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