Whakaoti i te n^2+16n+63

$$n ^ { 2 } + 16 n + 63$$

Tauwehe

$$\left(n+7\right)\left(n+9\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei n^{2}+an+bn+63. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=16 ab=1\times 63=63$$

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 63.

$$1,63 3,21 7,9$$

Tātaihia te tapeke mō ia takirua.

$$1+63=64 3+21=24 7+9=16$$

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

$$a=7 b=9$$

Tuhia anō te n^{2}+16n+63 hei \left(n^{2}+7n\right)+\left(9n+63\right).

$$\left(n^{2}+7n\right)+\left(9n+63\right)$$

Tauwehea te n i te tuatahi me te 9 i te rōpū tuarua.

$$n\left(n+7\right)+9\left(n+7\right)$$

Whakatauwehea atu te kīanga pātahi n+7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(n+7\right)\left(n+9\right)$$

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.

$$n^{2}+16n+63=0$$

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.

$$n=\frac{-16±\sqrt{16^{2}-4\times 63}}{2}$$

Pūrua 16.

$$n=\frac{-16±\sqrt{256-4\times 63}}{2}$$

Whakareatia -4 ki te 63.

$$n=\frac{-16±\sqrt{256-252}}{2}$$

Tāpiri 256 ki te -252.

$$n=\frac{-16±\sqrt{4}}{2}$$

Tuhia te pūtakerua o te 4.

$$n=\frac{-16±2}{2}$$

Nā, me whakaoti te whārite n=\frac{-16±2}{2} ina he tāpiri te ±. Tāpiri -16 ki te 2.

$$n=-\frac{14}{2}$$

Whakawehe -14 ki te 2.

$$n=-7$$

Nā, me whakaoti te whārite n=\frac{-16±2}{2} ina he tango te ±. Tango 2 mai i -16.

$$n=-\frac{18}{2}$$

Whakawehe -18 ki te 2.

$$n=-9$$

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 -7 mō te x_{1} me te -9 mō te x_{2}.

$$n^{2}+16n+63=\left(n-\left(-7\right)\right)\left(n-\left(-9\right)\right)$$

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

$$n^{2}+16n+63=\left(n+7\right)\left(n+9\right)$$

Aromātai

$$\left(n+7\right)\left(n+9\right)$$