Whakaoti i te a^2+7a-60=

$$a ^ { 2 } + 7 a - 60 =$$

Tauwehe

$$\left(a-5\right)\left(a+12\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei a^{2}+pa+qa-60. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=7 pq=1\left(-60\right)=-60$$

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 -60.

$$-1,60 -2,30 -3,20 -4,15 -5,12 -6,10$$

Tātaihia te tapeke mō ia takirua.

$$-1+60=59 -2+30=28 -3+20=17 -4+15=11 -5+12=7 -6+10=4$$

Ko te otinga te takirua ka hoatu i te tapeke 7.

$$p=-5 q=12$$

Tuhia anō te a^{2}+7a-60 hei \left(a^{2}-5a\right)+\left(12a-60\right).

$$\left(a^{2}-5a\right)+\left(12a-60\right)$$

Tauwehea te a i te tuatahi me te 12 i te rōpū tuarua.

$$a\left(a-5\right)+12\left(a-5\right)$$

Whakatauwehea atu te kīanga pātahi a-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(a-5\right)\left(a+12\right)$$

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.

$$a^{2}+7a-60=0$$

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.

$$a=\frac{-7±\sqrt{7^{2}-4\left(-60\right)}}{2}$$

Pūrua 7.

$$a=\frac{-7±\sqrt{49-4\left(-60\right)}}{2}$$

Whakareatia -4 ki te -60.

$$a=\frac{-7±\sqrt{49+240}}{2}$$

Tāpiri 49 ki te 240.

$$a=\frac{-7±\sqrt{289}}{2}$$

Tuhia te pūtakerua o te 289.

$$a=\frac{-7±17}{2}$$

Nā, me whakaoti te whārite a=\frac{-7±17}{2} ina he tāpiri te ±. Tāpiri -7 ki te 17.

$$a=\frac{10}{2}$$

Whakawehe 10 ki te 2.

$$a=5$$

Nā, me whakaoti te whārite a=\frac{-7±17}{2} ina he tango te ±. Tango 17 mai i -7.

$$a=-\frac{24}{2}$$

Whakawehe -24 ki te 2.

$$a=-12$$

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 5 mō te x_{1} me te -12 mō te x_{2}.

$$a^{2}+7a-60=\left(a-5\right)\left(a-\left(-12\right)\right)$$

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

$$a^{2}+7a-60=\left(a-5\right)\left(a+12\right)$$

Aromātai

$$\left(a-5\right)\left(a+12\right)$$