Whakaoti i te x^2+6x-91

$${ x }^{ 2 } +6x-91$$

Tauwehe

$$\left(x-7\right)\left(x+13\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-91. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=1\left(-91\right)=-91$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, 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 -91.

$$-1,91 -7,13$$

Tātaihia te tapeke mō ia takirua.

$$-1+91=90 -7+13=6$$

Ko te otinga te takirua ka hoatu i te tapeke 6.

$$a=-7 b=13$$

Tuhia anō te x^{2}+6x-91 hei \left(x^{2}-7x\right)+\left(13x-91\right).

$$\left(x^{2}-7x\right)+\left(13x-91\right)$$

Tauwehea te x i te tuatahi me te 13 i te rōpū tuarua.

$$x\left(x-7\right)+13\left(x-7\right)$$

Whakatauwehea atu te kīanga pātahi x-7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-7\right)\left(x+13\right)$$

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.

$$x^{2}+6x-91=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-91\right)}}{2}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\left(-91\right)}}{2}$$

Whakareatia -4 ki te -91.

$$x=\frac{-6±\sqrt{36+364}}{2}$$

Tāpiri 36 ki te 364.

$$x=\frac{-6±\sqrt{400}}{2}$$

Tuhia te pūtakerua o te 400.

$$x=\frac{-6±20}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±20}{2} ina he tāpiri te ±. Tāpiri -6 ki te 20.

$$x=\frac{14}{2}$$

Whakawehe 14 ki te 2.

$$x=7$$

Nā, me whakaoti te whārite x=\frac{-6±20}{2} ina he tango te ±. Tango 20 mai i -6.

$$x=-\frac{26}{2}$$

Whakawehe -26 ki te 2.

$$x=-13$$

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 7 mō te x_{1} me te -13 mō te x_{2}.

$$x^{2}+6x-91=\left(x-7\right)\left(x-\left(-13\right)\right)$$

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

$$x^{2}+6x-91=\left(x-7\right)\left(x+13\right)$$

Aromātai

$$\left(x-7\right)\left(x+13\right)$$