Whakaoti i te x^2-11x+18

$$x ^ { 2 } - 11 x + 18$$

Tauwehe

$$\left(x-9\right)\left(x-2\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+18. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-11 ab=1\times 18=18$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 18.

$$-1,-18 -2,-9 -3,-6$$

Tātaihia te tapeke mō ia takirua.

$$-1-18=-19 -2-9=-11 -3-6=-9$$

Ko te otinga te takirua ka hoatu i te tapeke -11.

$$a=-9 b=-2$$

Tuhia anō te x^{2}-11x+18 hei \left(x^{2}-9x\right)+\left(-2x+18\right).

$$\left(x^{2}-9x\right)+\left(-2x+18\right)$$

Tauwehea te x i te tuatahi me te -2 i te rōpū tuarua.

$$x\left(x-9\right)-2\left(x-9\right)$$

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

$$\left(x-9\right)\left(x-2\right)$$

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.

$$x^{2}-11x+18=0$$

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.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 18}}{2}$$

Pūrua -11.

$$x=\frac{-\left(-11\right)±\sqrt{121-4\times 18}}{2}$$

Whakareatia -4 ki te 18.

$$x=\frac{-\left(-11\right)±\sqrt{121-72}}{2}$$

Tāpiri 121 ki te -72.

$$x=\frac{-\left(-11\right)±\sqrt{49}}{2}$$

Tuhia te pūtakerua o te 49.

$$x=\frac{-\left(-11\right)±7}{2}$$

Ko te tauaro o -11 ko 11.

$$x=\frac{11±7}{2}$$

Nā, me whakaoti te whārite x=\frac{11±7}{2} ina he tāpiri te ±. Tāpiri 11 ki te 7.

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

Whakawehe 18 ki te 2.

$$x=9$$

Nā, me whakaoti te whārite x=\frac{11±7}{2} ina he tango te ±. Tango 7 mai i 11.

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

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 9 mō te x_{1} me te 2 mō te x_{2}.

$$x^{2}-11x+18=\left(x-9\right)\left(x-2\right)$$

Aromātai

$$\left(x-9\right)\left(x-2\right)$$