Whakaoti i te y^2+y-110=

$$y ^ { 2 } + y - 110 =$$

Tauwehe

$$\left(y-10\right)\left(y+11\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei y^{2}+ay+by-110. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=1\left(-110\right)=-110$$

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 -110.

$$-1,110 -2,55 -5,22 -10,11$$

Tātaihia te tapeke mō ia takirua.

$$-1+110=109 -2+55=53 -5+22=17 -10+11=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=-10 b=11$$

Tuhia anō te y^{2}+y-110 hei \left(y^{2}-10y\right)+\left(11y-110\right).

$$\left(y^{2}-10y\right)+\left(11y-110\right)$$

Tauwehea te y i te tuatahi me te 11 i te rōpū tuarua.

$$y\left(y-10\right)+11\left(y-10\right)$$

Whakatauwehea atu te kīanga pātahi y-10 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(y-10\right)\left(y+11\right)$$

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.

$$y^{2}+y-110=0$$

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.

$$y=\frac{-1±\sqrt{1^{2}-4\left(-110\right)}}{2}$$

Pūrua 1.

$$y=\frac{-1±\sqrt{1-4\left(-110\right)}}{2}$$

Whakareatia -4 ki te -110.

$$y=\frac{-1±\sqrt{1+440}}{2}$$

Tāpiri 1 ki te 440.

$$y=\frac{-1±\sqrt{441}}{2}$$

Tuhia te pūtakerua o te 441.

$$y=\frac{-1±21}{2}$$

Nā, me whakaoti te whārite y=\frac{-1±21}{2} ina he tāpiri te ±. Tāpiri -1 ki te 21.

$$y=\frac{20}{2}$$

Whakawehe 20 ki te 2.

$$y=10$$

Nā, me whakaoti te whārite y=\frac{-1±21}{2} ina he tango te ±. Tango 21 mai i -1.

$$y=-\frac{22}{2}$$

Whakawehe -22 ki te 2.

$$y=-11$$

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 10 mō te x_{1} me te -11 mō te x_{2}.

$$y^{2}+y-110=\left(y-10\right)\left(y-\left(-11\right)\right)$$

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

$$y^{2}+y-110=\left(y-10\right)\left(y+11\right)$$

Aromātai

$$\left(y-10\right)\left(y+11\right)$$