Whakaoti i te m^2-21m-72

$$m ^ { 2 } - 21 m - 72$$

Tauwehe

$$\left(m-24\right)\left(m+3\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei m^{2}+am+bm-72. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-21 ab=1\left(-72\right)=-72$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -72.

$$1,-72 2,-36 3,-24 4,-18 6,-12 8,-9$$

Tātaihia te tapeke mō ia takirua.

$$1-72=-71 2-36=-34 3-24=-21 4-18=-14 6-12=-6 8-9=-1$$

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

$$a=-24 b=3$$

Tuhia anō te m^{2}-21m-72 hei \left(m^{2}-24m\right)+\left(3m-72\right).

$$\left(m^{2}-24m\right)+\left(3m-72\right)$$

Tauwehea te m i te tuatahi me te 3 i te rōpū tuarua.

$$m\left(m-24\right)+3\left(m-24\right)$$

Whakatauwehea atu te kīanga pātahi m-24 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(m-24\right)\left(m+3\right)$$

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.

$$m^{2}-21m-72=0$$

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.

$$m=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}-4\left(-72\right)}}{2}$$

Pūrua -21.

$$m=\frac{-\left(-21\right)±\sqrt{441-4\left(-72\right)}}{2}$$

Whakareatia -4 ki te -72.

$$m=\frac{-\left(-21\right)±\sqrt{441+288}}{2}$$

Tāpiri 441 ki te 288.

$$m=\frac{-\left(-21\right)±\sqrt{729}}{2}$$

Tuhia te pūtakerua o te 729.

$$m=\frac{-\left(-21\right)±27}{2}$$

Ko te tauaro o -21 ko 21.

$$m=\frac{21±27}{2}$$

Nā, me whakaoti te whārite m=\frac{21±27}{2} ina he tāpiri te ±. Tāpiri 21 ki te 27.

$$m=\frac{48}{2}$$

Whakawehe 48 ki te 2.

$$m=24$$

Nā, me whakaoti te whārite m=\frac{21±27}{2} ina he tango te ±. Tango 27 mai i 21.

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

Whakawehe -6 ki te 2.

$$m=-3$$

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 24 mō te x_{1} me te -3 mō te x_{2}.

$$m^{2}-21m-72=\left(m-24\right)\left(m-\left(-3\right)\right)$$

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

$$m^{2}-21m-72=\left(m-24\right)\left(m+3\right)$$

Aromātai

$$\left(m-24\right)\left(m+3\right)$$