Whakaoti i te y^2+15y+44

$${ y }^{ 2 } +15y+44$$

Tauwehe

$$\left(y+4\right)\left(y+11\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei y^{2}+ay+by+44. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=15 ab=1\times 44=44$$

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 44.

$$1,44 2,22 4,11$$

Tātaihia te tapeke mō ia takirua.

$$1+44=45 2+22=24 4+11=15$$

Ko te otinga te takirua ka hoatu i te tapeke 15.

$$a=4 b=11$$

Tuhia anō te y^{2}+15y+44 hei \left(y^{2}+4y\right)+\left(11y+44\right).

$$\left(y^{2}+4y\right)+\left(11y+44\right)$$

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

$$y\left(y+4\right)+11\left(y+4\right)$$

Whakatauwehea atu te kīanga pātahi y+4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(y+4\right)\left(y+11\right)$$

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.

$$y^{2}+15y+44=0$$

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.

$$y=\frac{-15±\sqrt{15^{2}-4\times 44}}{2}$$

Pūrua 15.

$$y=\frac{-15±\sqrt{225-4\times 44}}{2}$$

Whakareatia -4 ki te 44.

$$y=\frac{-15±\sqrt{225-176}}{2}$$

Tāpiri 225 ki te -176.

$$y=\frac{-15±\sqrt{49}}{2}$$

Tuhia te pūtakerua o te 49.

$$y=\frac{-15±7}{2}$$

Nā, me whakaoti te whārite y=\frac{-15±7}{2} ina he tāpiri te ±. Tāpiri -15 ki te 7.

$$y=-\frac{8}{2}$$

Whakawehe -8 ki te 2.

$$y=-4$$

Nā, me whakaoti te whārite y=\frac{-15±7}{2} ina he tango te ±. Tango 7 mai i -15.

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

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 -4 mō te x_{1} me te -11 mō te x_{2}.

$$y^{2}+15y+44=\left(y-\left(-4\right)\right)\left(y-\left(-11\right)\right)$$

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

$$y^{2}+15y+44=\left(y+4\right)\left(y+11\right)$$

Aromātai

$$\left(y+4\right)\left(y+11\right)$$