Whakaoti i te y^2+9y+18

$$y ^ { 2 } + 9 y + 18$$

Tauwehe

$$\left(y+3\right)\left(y+6\right)$$

Ngā Upane Otinga

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

$$a+b=9 ab=1\times 18=18$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga 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 9.

$$a=3 b=6$$

Tuhia anō te y^{2}+9y+18 hei \left(y^{2}+3y\right)+\left(6y+18\right).

$$\left(y^{2}+3y\right)+\left(6y+18\right)$$

Tauwehea te y i te tuatahi me te 6 i te rōpū tuarua.

$$y\left(y+3\right)+6\left(y+3\right)$$

Whakatauwehea atu te kīanga pātahi y+3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(y+3\right)\left(y+6\right)$$

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.

$$y^{2}+9y+18=0$$

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.

$$y=\frac{-9±\sqrt{9^{2}-4\times 18}}{2}$$

Pūrua 9.

$$y=\frac{-9±\sqrt{81-4\times 18}}{2}$$

Whakareatia -4 ki te 18.

$$y=\frac{-9±\sqrt{81-72}}{2}$$

Tāpiri 81 ki te -72.

$$y=\frac{-9±\sqrt{9}}{2}$$

Tuhia te pūtakerua o te 9.

$$y=\frac{-9±3}{2}$$

Nā, me whakaoti te whārite y=\frac{-9±3}{2} ina he tāpiri te ±. Tāpiri -9 ki te 3.

$$y=-\frac{6}{2}$$

Whakawehe -6 ki te 2.

$$y=-3$$

Nā, me whakaoti te whārite y=\frac{-9±3}{2} ina he tango te ±. Tango 3 mai i -9.

$$y=-\frac{12}{2}$$

Whakawehe -12 ki te 2.

$$y=-6$$

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 -3 mō te x_{1} me te -6 mō te x_{2}.

$$y^{2}+9y+18=\left(y-\left(-3\right)\right)\left(y-\left(-6\right)\right)$$

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

$$y^{2}+9y+18=\left(y+3\right)\left(y+6\right)$$

Aromātai

$$\left(y+3\right)\left(y+6\right)$$