Whakaoti i te n^2+21n+98

$$n ^ { 2 } + 21 n + 98$$

Tauwehe

$$\left(n+7\right)\left(n+14\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei n^{2}+an+bn+98. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=21 ab=1\times 98=98$$

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 98.

$$1,98 2,49 7,14$$

Tātaihia te tapeke mō ia takirua.

$$1+98=99 2+49=51 7+14=21$$

Ko te otinga te takirua ka hoatu i te tapeke 21.

$$a=7 b=14$$

Tuhia anō te n^{2}+21n+98 hei \left(n^{2}+7n\right)+\left(14n+98\right).

$$\left(n^{2}+7n\right)+\left(14n+98\right)$$

Tauwehea te n i te tuatahi me te 14 i te rōpū tuarua.

$$n\left(n+7\right)+14\left(n+7\right)$$

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

$$\left(n+7\right)\left(n+14\right)$$

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.

$$n^{2}+21n+98=0$$

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.

$$n=\frac{-21±\sqrt{21^{2}-4\times 98}}{2}$$

Pūrua 21.

$$n=\frac{-21±\sqrt{441-4\times 98}}{2}$$

Whakareatia -4 ki te 98.

$$n=\frac{-21±\sqrt{441-392}}{2}$$

Tāpiri 441 ki te -392.

$$n=\frac{-21±\sqrt{49}}{2}$$

Tuhia te pūtakerua o te 49.

$$n=\frac{-21±7}{2}$$

Nā, me whakaoti te whārite n=\frac{-21±7}{2} ina he tāpiri te ±. Tāpiri -21 ki te 7.

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

Whakawehe -14 ki te 2.

$$n=-7$$

Nā, me whakaoti te whārite n=\frac{-21±7}{2} ina he tango te ±. Tango 7 mai i -21.

$$n=-\frac{28}{2}$$

Whakawehe -28 ki te 2.

$$n=-14$$

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 -14 mō te x_{2}.

$$n^{2}+21n+98=\left(n-\left(-7\right)\right)\left(n-\left(-14\right)\right)$$

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

$$n^{2}+21n+98=\left(n+7\right)\left(n+14\right)$$

Aromātai

$$\left(n+7\right)\left(n+14\right)$$