Whakaoti i te 33+8a-a^2

$$33 + 8 a - a ^ { 2 }$$

Tauwehe

$$-\left(a-11\right)\left(a+3\right)$$

Ngā Upane Otinga

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-a^{2}+8a+33$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -a^{2}+pa+qa+33. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=8 pq=-33=-33$$

I te mea kua tōraro te pq, he tauaro ngā tohu o p me q. I te mea kua tōrunga te p+q, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -33.

$$-1,33 -3,11$$

Tātaihia te tapeke mō ia takirua.

$$-1+33=32 -3+11=8$$

Ko te otinga te takirua ka hoatu i te tapeke 8.

$$p=11 q=-3$$

Tuhia anō te -a^{2}+8a+33 hei \left(-a^{2}+11a\right)+\left(-3a+33\right).

$$\left(-a^{2}+11a\right)+\left(-3a+33\right)$$

Tauwehea te -a i te tuatahi me te -3 i te rōpū tuarua.

$$-a\left(a-11\right)-3\left(a-11\right)$$

Whakatauwehea atu te kīanga pātahi a-11 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(a-11\right)\left(-a-3\right)$$

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.

$$-a^{2}+8a+33=0$$

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.

$$a=\frac{-8±\sqrt{8^{2}-4\left(-1\right)\times 33}}{2\left(-1\right)}$$

Pūrua 8.

$$a=\frac{-8±\sqrt{64-4\left(-1\right)\times 33}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$a=\frac{-8±\sqrt{64+4\times 33}}{2\left(-1\right)}$$

Whakareatia 4 ki te 33.

$$a=\frac{-8±\sqrt{64+132}}{2\left(-1\right)}$$

Tāpiri 64 ki te 132.

$$a=\frac{-8±\sqrt{196}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 196.

$$a=\frac{-8±14}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$a=\frac{-8±14}{-2}$$

Nā, me whakaoti te whārite a=\frac{-8±14}{-2} ina he tāpiri te ±. Tāpiri -8 ki te 14.

$$a=\frac{6}{-2}$$

Whakawehe 6 ki te -2.

$$a=-3$$

Nā, me whakaoti te whārite a=\frac{-8±14}{-2} ina he tango te ±. Tango 14 mai i -8.

$$a=-\frac{22}{-2}$$

Whakawehe -22 ki te -2.

$$a=11$$

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 11 mō te x_{2}.

$$-a^{2}+8a+33=-\left(a-\left(-3\right)\right)\left(a-11\right)$$

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

$$-a^{2}+8a+33=-\left(a+3\right)\left(a-11\right)$$

Aromātai

$$-\left(a-11\right)\left(a+3\right)$$