Whakaoti i te A+2-A^2

$$A + 2 - A ^ { 2 }$$

Tauwehe

$$-\left(A-2\right)\left(A+1\right)$$

Ngā Upane Otinga

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-A^{2}+A+2$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -A^{2}+aA+bA+2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=-2=-2$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=2 b=-1$$

Tuhia anō te -A^{2}+A+2 hei \left(-A^{2}+2A\right)+\left(-A+2\right).

$$\left(-A^{2}+2A\right)+\left(-A+2\right)$$

Tauwehea te -A i te tuatahi me te -1 i te rōpū tuarua.

$$-A\left(A-2\right)-\left(A-2\right)$$

Whakatauwehea atu te kīanga pātahi A-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(A-2\right)\left(-A-1\right)$$

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.

$$-A^{2}+A+2=0$$

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.

$$A=\frac{-1±\sqrt{1^{2}-4\left(-1\right)\times 2}}{2\left(-1\right)}$$

Pūrua 1.

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

Whakareatia -4 ki te -1.

$$A=\frac{-1±\sqrt{1+4\times 2}}{2\left(-1\right)}$$

Whakareatia 4 ki te 2.

$$A=\frac{-1±\sqrt{1+8}}{2\left(-1\right)}$$

Tāpiri 1 ki te 8.

$$A=\frac{-1±\sqrt{9}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 9.

$$A=\frac{-1±3}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$A=\frac{-1±3}{-2}$$

Nā, me whakaoti te whārite A=\frac{-1±3}{-2} ina he tāpiri te ±. Tāpiri -1 ki te 3.

$$A=\frac{2}{-2}$$

Whakawehe 2 ki te -2.

$$A=-1$$

Nā, me whakaoti te whārite A=\frac{-1±3}{-2} ina he tango te ±. Tango 3 mai i -1.

$$A=-\frac{4}{-2}$$

Whakawehe -4 ki te -2.

$$A=2$$

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 -1 mō te x_{1} me te 2 mō te x_{2}.

$$-A^{2}+A+2=-\left(A-\left(-1\right)\right)\left(A-2\right)$$

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

$$-A^{2}+A+2=-\left(A+1\right)\left(A-2\right)$$

Aromātai

$$-\left(A-2\right)\left(A+1\right)$$