Whakaoti i te m^2-13m+36

$$m ^ { 2 } - 13 m + 36$$

Tauwehe

$$\left(m-9\right)\left(m-4\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei m^{2}+am+bm+36. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-13 ab=1\times 36=36$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 36.

$$-1,-36 -2,-18 -3,-12 -4,-9 -6,-6$$

Tātaihia te tapeke mō ia takirua.

$$-1-36=-37 -2-18=-20 -3-12=-15 -4-9=-13 -6-6=-12$$

Ko te otinga te takirua ka hoatu i te tapeke -13.

$$a=-9 b=-4$$

Tuhia anō te m^{2}-13m+36 hei \left(m^{2}-9m\right)+\left(-4m+36\right).

$$\left(m^{2}-9m\right)+\left(-4m+36\right)$$

Tauwehea te m i te tuatahi me te -4 i te rōpū tuarua.

$$m\left(m-9\right)-4\left(m-9\right)$$

Whakatauwehea atu te kīanga pātahi m-9 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(m-9\right)\left(m-4\right)$$

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.

$$m^{2}-13m+36=0$$

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.

$$m=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 36}}{2}$$

Pūrua -13.

$$m=\frac{-\left(-13\right)±\sqrt{169-4\times 36}}{2}$$

Whakareatia -4 ki te 36.

$$m=\frac{-\left(-13\right)±\sqrt{169-144}}{2}$$

Tāpiri 169 ki te -144.

$$m=\frac{-\left(-13\right)±\sqrt{25}}{2}$$

Tuhia te pūtakerua o te 25.

$$m=\frac{-\left(-13\right)±5}{2}$$

Ko te tauaro o -13 ko 13.

$$m=\frac{13±5}{2}$$

Nā, me whakaoti te whārite m=\frac{13±5}{2} ina he tāpiri te ±. Tāpiri 13 ki te 5.

$$m=\frac{18}{2}$$

Whakawehe 18 ki te 2.

$$m=9$$

Nā, me whakaoti te whārite m=\frac{13±5}{2} ina he tango te ±. Tango 5 mai i 13.

$$m=\frac{8}{2}$$

Whakawehe 8 ki te 2.

$$m=4$$

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 9 mō te x_{1} me te 4 mō te x_{2}.

$$m^{2}-13m+36=\left(m-9\right)\left(m-4\right)$$

Aromātai

$$\left(m-9\right)\left(m-4\right)$$