Whakaoti i te y^2+15y+50

$$y ^ { 2 } + 15 y + 50$$

Tauwehe

$$\left(y+5\right)\left(y+10\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei y^{2}+ay+by+50. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=15 ab=1\times 50=50$$

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 50.

$$1,50 2,25 5,10$$

Tātaihia te tapeke mō ia takirua.

$$1+50=51 2+25=27 5+10=15$$

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

$$a=5 b=10$$

Tuhia anō te y^{2}+15y+50 hei \left(y^{2}+5y\right)+\left(10y+50\right).

$$\left(y^{2}+5y\right)+\left(10y+50\right)$$

Tauwehea te y i te tuatahi me te 10 i te rōpū tuarua.

$$y\left(y+5\right)+10\left(y+5\right)$$

Whakatauwehea atu te kīanga pātahi y+5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(y+5\right)\left(y+10\right)$$

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.

$$y^{2}+15y+50=0$$

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.

$$y=\frac{-15±\sqrt{15^{2}-4\times 50}}{2}$$

Pūrua 15.

$$y=\frac{-15±\sqrt{225-4\times 50}}{2}$$

Whakareatia -4 ki te 50.

$$y=\frac{-15±\sqrt{225-200}}{2}$$

Tāpiri 225 ki te -200.

$$y=\frac{-15±\sqrt{25}}{2}$$

Tuhia te pūtakerua o te 25.

$$y=\frac{-15±5}{2}$$

Nā, me whakaoti te whārite y=\frac{-15±5}{2} ina he tāpiri te ±. Tāpiri -15 ki te 5.

$$y=-\frac{10}{2}$$

Whakawehe -10 ki te 2.

$$y=-5$$

Nā, me whakaoti te whārite y=\frac{-15±5}{2} ina he tango te ±. Tango 5 mai i -15.

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

Whakawehe -20 ki te 2.

$$y=-10$$

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 -5 mō te x_{1} me te -10 mō te x_{2}.

$$y^{2}+15y+50=\left(y-\left(-5\right)\right)\left(y-\left(-10\right)\right)$$

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

$$y^{2}+15y+50=\left(y+5\right)\left(y+10\right)$$

Aromātai

$$\left(y+5\right)\left(y+10\right)$$