Whakaoti i te y^2+6y-7

$$y ^ { 2 } + 6 y - 7$$

Tauwehe

$$\left(y-1\right)\left(y+7\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei y^{2}+ay+by-7. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=1\left(-7\right)=-7$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-1 b=7$$

Tuhia anō te y^{2}+6y-7 hei \left(y^{2}-y\right)+\left(7y-7\right).

$$\left(y^{2}-y\right)+\left(7y-7\right)$$

Tauwehea te y i te tuatahi me te 7 i te rōpū tuarua.

$$y\left(y-1\right)+7\left(y-1\right)$$

Whakatauwehea atu te kīanga pātahi y-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(y-1\right)\left(y+7\right)$$

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.

$$y^{2}+6y-7=0$$

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.

$$y=\frac{-6±\sqrt{6^{2}-4\left(-7\right)}}{2}$$

Pūrua 6.

$$y=\frac{-6±\sqrt{36-4\left(-7\right)}}{2}$$

Whakareatia -4 ki te -7.

$$y=\frac{-6±\sqrt{36+28}}{2}$$

Tāpiri 36 ki te 28.

$$y=\frac{-6±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$y=\frac{-6±8}{2}$$

Nā, me whakaoti te whārite y=\frac{-6±8}{2} ina he tāpiri te ±. Tāpiri -6 ki te 8.

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

Whakawehe 2 ki te 2.

$$y=1$$

Nā, me whakaoti te whārite y=\frac{-6±8}{2} ina he tango te ±. Tango 8 mai i -6.

$$y=-\frac{14}{2}$$

Whakawehe -14 ki te 2.

$$y=-7$$

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 1 mō te x_{1} me te -7 mō te x_{2}.

$$y^{2}+6y-7=\left(y-1\right)\left(y-\left(-7\right)\right)$$

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

$$y^{2}+6y-7=\left(y-1\right)\left(y+7\right)$$

Aromātai

$$\left(y-1\right)\left(y+7\right)$$