Whakaoti i te a^2+10a-600

$$a ^ { 2 } + 10 a - 600$$

Tauwehe

$$\left(a-20\right)\left(a+30\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei a^{2}+pa+qa-600. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=10 pq=1\left(-600\right)=-600$$

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 -600.

$$-1,600 -2,300 -3,200 -4,150 -5,120 -6,100 -8,75 -10,60 -12,50 -15,40 -20,30 -24,25$$

Tātaihia te tapeke mō ia takirua.

$$-1+600=599 -2+300=298 -3+200=197 -4+150=146 -5+120=115 -6+100=94 -8+75=67 -10+60=50 -12+50=38 -15+40=25 -20+30=10 -24+25=1$$

Ko te otinga te takirua ka hoatu i te tapeke 10.

$$p=-20 q=30$$

Tuhia anō te a^{2}+10a-600 hei \left(a^{2}-20a\right)+\left(30a-600\right).

$$\left(a^{2}-20a\right)+\left(30a-600\right)$$

Tauwehea te a i te tuatahi me te 30 i te rōpū tuarua.

$$a\left(a-20\right)+30\left(a-20\right)$$

Whakatauwehea atu te kīanga pātahi a-20 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(a-20\right)\left(a+30\right)$$

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.

$$a^{2}+10a-600=0$$

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.

$$a=\frac{-10±\sqrt{10^{2}-4\left(-600\right)}}{2}$$

Pūrua 10.

$$a=\frac{-10±\sqrt{100-4\left(-600\right)}}{2}$$

Whakareatia -4 ki te -600.

$$a=\frac{-10±\sqrt{100+2400}}{2}$$

Tāpiri 100 ki te 2400.

$$a=\frac{-10±\sqrt{2500}}{2}$$

Tuhia te pūtakerua o te 2500.

$$a=\frac{-10±50}{2}$$

Nā, me whakaoti te whārite a=\frac{-10±50}{2} ina he tāpiri te ±. Tāpiri -10 ki te 50.

$$a=\frac{40}{2}$$

Whakawehe 40 ki te 2.

$$a=20$$

Nā, me whakaoti te whārite a=\frac{-10±50}{2} ina he tango te ±. Tango 50 mai i -10.

$$a=-\frac{60}{2}$$

Whakawehe -60 ki te 2.

$$a=-30$$

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 20 mō te x_{1} me te -30 mō te x_{2}.

$$a^{2}+10a-600=\left(a-20\right)\left(a-\left(-30\right)\right)$$

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

$$a^{2}+10a-600=\left(a-20\right)\left(a+30\right)$$

Aromātai

$$\left(a-20\right)\left(a+30\right)$$