Whakaoti i te x^2-16x+63

$$x ^ { 2 } - 16 x + 63$$

Tauwehe

$$\left(x-9\right)\left(x-7\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+63. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-16 ab=1\times 63=63$$

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 63.

$$-1,-63 -3,-21 -7,-9$$

Tātaihia te tapeke mō ia takirua.

$$-1-63=-64 -3-21=-24 -7-9=-16$$

Ko te otinga te takirua ka hoatu i te tapeke -16.

$$a=-9 b=-7$$

Tuhia anō te x^{2}-16x+63 hei \left(x^{2}-9x\right)+\left(-7x+63\right).

$$\left(x^{2}-9x\right)+\left(-7x+63\right)$$

Tauwehea te x i te tuatahi me te -7 i te rōpū tuarua.

$$x\left(x-9\right)-7\left(x-9\right)$$

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

$$\left(x-9\right)\left(x-7\right)$$

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.

$$x^{2}-16x+63=0$$

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.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}-4\times 63}}{2}$$

Pūrua -16.

$$x=\frac{-\left(-16\right)±\sqrt{256-4\times 63}}{2}$$

Whakareatia -4 ki te 63.

$$x=\frac{-\left(-16\right)±\sqrt{256-252}}{2}$$

Tāpiri 256 ki te -252.

$$x=\frac{-\left(-16\right)±\sqrt{4}}{2}$$

Tuhia te pūtakerua o te 4.

$$x=\frac{-\left(-16\right)±2}{2}$$

Ko te tauaro o -16 ko 16.

$$x=\frac{16±2}{2}$$

Nā, me whakaoti te whārite x=\frac{16±2}{2} ina he tāpiri te ±. Tāpiri 16 ki te 2.

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

Whakawehe 18 ki te 2.

$$x=9$$

Nā, me whakaoti te whārite x=\frac{16±2}{2} ina he tango te ±. Tango 2 mai i 16.

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

Whakawehe 14 ki te 2.

$$x=7$$

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 7 mō te x_{2}.

$$x^{2}-16x+63=\left(x-9\right)\left(x-7\right)$$

Aromātai

$$\left(x-9\right)\left(x-7\right)$$