Whakaoti i te x^2-x-72

$$x ^ { 2 } - x - 72$$

Tauwehe

$$\left(x-9\right)\left(x+8\right)$$

Ngā Upane Otinga

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

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

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 -1.

$$a=-9 b=8$$

Tuhia anō te x^{2}-x-72 hei \left(x^{2}-9x\right)+\left(8x-72\right).

$$\left(x^{2}-9x\right)+\left(8x-72\right)$$

Tauwehea te x i te tuatahi me te 8 i te rōpū tuarua.

$$x\left(x-9\right)+8\left(x-9\right)$$

Whakatauwehea atu te kīanga pātahi x-9 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-9\right)\left(x+8\right)$$

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.

$$x^{2}-x-72=0$$

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.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\left(-72\right)}}{2}$$

Whakareatia -4 ki te -72.

$$x=\frac{-\left(-1\right)±\sqrt{1+288}}{2}$$

Tāpiri 1 ki te 288.

$$x=\frac{-\left(-1\right)±\sqrt{289}}{2}$$

Tuhia te pūtakerua o te 289.

$$x=\frac{-\left(-1\right)±17}{2}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±17}{2}$$

Nā, me whakaoti te whārite x=\frac{1±17}{2} ina he tāpiri te ±. Tāpiri 1 ki te 17.

$$x=\frac{18}{2}$$

Whakawehe 18 ki te 2.

$$x=9$$

Nā, me whakaoti te whārite x=\frac{1±17}{2} ina he tango te ±. Tango 17 mai i 1.

$$x=-\frac{16}{2}$$

Whakawehe -16 ki te 2.

$$x=-8$$

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 9 mō te x_{1} me te -8 mō te x_{2}.

$$x^{2}-x-72=\left(x-9\right)\left(x-\left(-8\right)\right)$$

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

$$x^{2}-x-72=\left(x-9\right)\left(x+8\right)$$

Aromātai

$$\left(x-9\right)\left(x+8\right)$$