Whakaoti i te 11+12m+m^2

$$11 + 12 m + m ^ { 2 }$$

Tauwehe

$$\left(m+1\right)\left(m+11\right)$$

Ngā Upane Otinga

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$m^{2}+12m+11$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei m^{2}+am+bm+11. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=12 ab=1\times 11=11$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=1 b=11$$

Tuhia anō te m^{2}+12m+11 hei \left(m^{2}+m\right)+\left(11m+11\right).

$$\left(m^{2}+m\right)+\left(11m+11\right)$$

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

$$m\left(m+1\right)+11\left(m+1\right)$$

Whakatauwehea atu te kīanga pātahi m+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(m+1\right)\left(m+11\right)$$

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.

$$m^{2}+12m+11=0$$

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.

$$m=\frac{-12±\sqrt{12^{2}-4\times 11}}{2}$$

Pūrua 12.

$$m=\frac{-12±\sqrt{144-4\times 11}}{2}$$

Whakareatia -4 ki te 11.

$$m=\frac{-12±\sqrt{144-44}}{2}$$

Tāpiri 144 ki te -44.

$$m=\frac{-12±\sqrt{100}}{2}$$

Tuhia te pūtakerua o te 100.

$$m=\frac{-12±10}{2}$$

Nā, me whakaoti te whārite m=\frac{-12±10}{2} ina he tāpiri te ±. Tāpiri -12 ki te 10.

$$m=-\frac{2}{2}$$

Whakawehe -2 ki te 2.

$$m=-1$$

Nā, me whakaoti te whārite m=\frac{-12±10}{2} ina he tango te ±. Tango 10 mai i -12.

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

Whakawehe -22 ki te 2.

$$m=-11$$

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

$$m^{2}+12m+11=\left(m-\left(-1\right)\right)\left(m-\left(-11\right)\right)$$

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

$$m^{2}+12m+11=\left(m+1\right)\left(m+11\right)$$

Aromātai

$$\left(m+1\right)\left(m+11\right)$$