Whakaoti i te 10m^2-m-9

$$10 m ^ { 2 } - m - 9$$

Tauwehe

$$\left(m-1\right)\left(10m+9\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 10m^{2}+am+bm-9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-1 ab=10\left(-9\right)=-90$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -90.

$$1,-90 2,-45 3,-30 5,-18 6,-15 9,-10$$

Tātaihia te tapeke mō ia takirua.

$$1-90=-89 2-45=-43 3-30=-27 5-18=-13 6-15=-9 9-10=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -1.

$$a=-10 b=9$$

Tuhia anō te 10m^{2}-m-9 hei \left(10m^{2}-10m\right)+\left(9m-9\right).

$$\left(10m^{2}-10m\right)+\left(9m-9\right)$$

Tauwehea te 10m i te tuatahi me te 9 i te rōpū tuarua.

$$10m\left(m-1\right)+9\left(m-1\right)$$

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

$$\left(m-1\right)\left(10m+9\right)$$

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.

$$10m^{2}-m-9=0$$

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.

$$m=\frac{-\left(-1\right)±\sqrt{1-4\times 10\left(-9\right)}}{2\times 10}$$

Whakareatia -4 ki te 10.

$$m=\frac{-\left(-1\right)±\sqrt{1-40\left(-9\right)}}{2\times 10}$$

Whakareatia -40 ki te -9.

$$m=\frac{-\left(-1\right)±\sqrt{1+360}}{2\times 10}$$

Tāpiri 1 ki te 360.

$$m=\frac{-\left(-1\right)±\sqrt{361}}{2\times 10}$$

Tuhia te pūtakerua o te 361.

$$m=\frac{-\left(-1\right)±19}{2\times 10}$$

Ko te tauaro o -1 ko 1.

$$m=\frac{1±19}{2\times 10}$$

Whakareatia 2 ki te 10.

$$m=\frac{1±19}{20}$$

Nā, me whakaoti te whārite m=\frac{1±19}{20} ina he tāpiri te ±. Tāpiri 1 ki te 19.

$$m=\frac{20}{20}$$

Whakawehe 20 ki te 20.

$$m=1$$

Nā, me whakaoti te whārite m=\frac{1±19}{20} ina he tango te ±. Tango 19 mai i 1.

$$m=-\frac{18}{20}$$

Whakahekea te hautanga \frac{-18}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$m=-\frac{9}{10}$$

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 1 mō te x_{1} me te -\frac{9}{10} mō te x_{2}.

$$10m^{2}-m-9=10\left(m-1\right)\left(m-\left(-\frac{9}{10}\right)\right)$$

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

$$10m^{2}-m-9=10\left(m-1\right)\left(m+\frac{9}{10}\right)$$

Tāpiri \frac{9}{10} ki te m mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$10m^{2}-m-9=10\left(m-1\right)\times \frac{10m+9}{10}$$

Whakakorea atu te tauwehe pūnoa nui rawa 10 i roto i te 10 me te 10.

$$10m^{2}-m-9=\left(m-1\right)\left(10m+9\right)$$

Aromātai

$$\left(m-1\right)\left(10m+9\right)$$