Whakaoti i te y^2+9y-36=

$$y ^ { 2 } + 9 y - 36 =$$

Tauwehe

$$\left(y-3\right)\left(y+12\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei y^{2}+ay+by-36. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=9 ab=1\left(-36\right)=-36$$

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. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -36.

$$-1,36 -2,18 -3,12 -4,9 -6,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+36=35 -2+18=16 -3+12=9 -4+9=5 -6+6=0$$

Ko te otinga te takirua ka hoatu i te tapeke 9.

$$a=-3 b=12$$

Tuhia anō te y^{2}+9y-36 hei \left(y^{2}-3y\right)+\left(12y-36\right).

$$\left(y^{2}-3y\right)+\left(12y-36\right)$$

Tauwehea te y i te tuatahi me te 12 i te rōpū tuarua.

$$y\left(y-3\right)+12\left(y-3\right)$$

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

$$\left(y-3\right)\left(y+12\right)$$

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.

$$y^{2}+9y-36=0$$

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.

$$y=\frac{-9±\sqrt{9^{2}-4\left(-36\right)}}{2}$$

Pūrua 9.

$$y=\frac{-9±\sqrt{81-4\left(-36\right)}}{2}$$

Whakareatia -4 ki te -36.

$$y=\frac{-9±\sqrt{81+144}}{2}$$

Tāpiri 81 ki te 144.

$$y=\frac{-9±\sqrt{225}}{2}$$

Tuhia te pūtakerua o te 225.

$$y=\frac{-9±15}{2}$$

Nā, me whakaoti te whārite y=\frac{-9±15}{2} ina he tāpiri te ±. Tāpiri -9 ki te 15.

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

Whakawehe 6 ki te 2.

$$y=3$$

Nā, me whakaoti te whārite y=\frac{-9±15}{2} ina he tango te ±. Tango 15 mai i -9.

$$y=-\frac{24}{2}$$

Whakawehe -24 ki te 2.

$$y=-12$$

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 -12 mō te x_{2}.

$$y^{2}+9y-36=\left(y-3\right)\left(y-\left(-12\right)\right)$$

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

$$y^{2}+9y-36=\left(y-3\right)\left(y+12\right)$$

Aromātai

$$\left(y-3\right)\left(y+12\right)$$