Whakaoti i te 10-3x-x^2

$$10 - 3 x - x ^ { 2 }$$

Tauwehe

$$\left(2-x\right)\left(x+5\right)$$

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.

$$-x^{2}-3x+10$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -x^{2}+ax+bx+10. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-3 ab=-10=-10$$

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 -10.

$$1,-10 2,-5$$

Tātaihia te tapeke mō ia takirua.

$$1-10=-9 2-5=-3$$

Ko te otinga te takirua ka hoatu i te tapeke -3.

$$a=2 b=-5$$

Tuhia anō te -x^{2}-3x+10 hei \left(-x^{2}+2x\right)+\left(-5x+10\right).

$$\left(-x^{2}+2x\right)+\left(-5x+10\right)$$

Tauwehea te x i te tuatahi me te 5 i te rōpū tuarua.

$$x\left(-x+2\right)+5\left(-x+2\right)$$

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

$$\left(-x+2\right)\left(x+5\right)$$

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.

$$-x^{2}-3x+10=0$$

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.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-1\right)\times 10}}{2\left(-1\right)}$$

Pūrua -3.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-1\right)\times 10}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-\left(-3\right)±\sqrt{9+4\times 10}}{2\left(-1\right)}$$

Whakareatia 4 ki te 10.

$$x=\frac{-\left(-3\right)±\sqrt{9+40}}{2\left(-1\right)}$$

Tāpiri 9 ki te 40.

$$x=\frac{-\left(-3\right)±\sqrt{49}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 49.

$$x=\frac{-\left(-3\right)±7}{2\left(-1\right)}$$

Ko te tauaro o -3 ko 3.

$$x=\frac{3±7}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{3±7}{-2}$$

Nā, me whakaoti te whārite x=\frac{3±7}{-2} ina he tāpiri te ±. Tāpiri 3 ki te 7.

$$x=\frac{10}{-2}$$

Whakawehe 10 ki te -2.

$$x=-5$$

Nā, me whakaoti te whārite x=\frac{3±7}{-2} ina he tango te ±. Tango 7 mai i 3.

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

Whakawehe -4 ki te -2.

$$x=2$$

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 -5 mō te x_{1} me te 2 mō te x_{2}.

$$-x^{2}-3x+10=-\left(x-\left(-5\right)\right)\left(x-2\right)$$

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

$$-x^{2}-3x+10=-\left(x+5\right)\left(x-2\right)$$

Aromātai

$$\left(2-x\right)\left(x+5\right)$$