Whakaoti i te 6g^2-39g+18

$$6 g ^ { 2 } - 39 g + 18$$

Tauwehe

$$3\left(g-6\right)\left(2g-1\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(2g^{2}-13g+6\right)$$

Whakaarohia te 2g^{2}-13g+6. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 2g^{2}+ag+bg+6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-13 ab=2\times 6=12$$

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 12.

$$-1,-12 -2,-6 -3,-4$$

Tātaihia te tapeke mō ia takirua.

$$-1-12=-13 -2-6=-8 -3-4=-7$$

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

$$a=-12 b=-1$$

Tuhia anō te 2g^{2}-13g+6 hei \left(2g^{2}-12g\right)+\left(-g+6\right).

$$\left(2g^{2}-12g\right)+\left(-g+6\right)$$

Tauwehea te 2g i te tuatahi me te -1 i te rōpū tuarua.

$$2g\left(g-6\right)-\left(g-6\right)$$

Whakatauwehea atu te kīanga pātahi g-6 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(g-6\right)\left(2g-1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3\left(g-6\right)\left(2g-1\right)$$

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.

$$6g^{2}-39g+18=0$$

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.

$$g=\frac{-\left(-39\right)±\sqrt{\left(-39\right)^{2}-4\times 6\times 18}}{2\times 6}$$

Pūrua -39.

$$g=\frac{-\left(-39\right)±\sqrt{1521-4\times 6\times 18}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$g=\frac{-\left(-39\right)±\sqrt{1521-24\times 18}}{2\times 6}$$

Whakareatia -24 ki te 18.

$$g=\frac{-\left(-39\right)±\sqrt{1521-432}}{2\times 6}$$

Tāpiri 1521 ki te -432.

$$g=\frac{-\left(-39\right)±\sqrt{1089}}{2\times 6}$$

Tuhia te pūtakerua o te 1089.

$$g=\frac{-\left(-39\right)±33}{2\times 6}$$

Ko te tauaro o -39 ko 39.

$$g=\frac{39±33}{2\times 6}$$

Whakareatia 2 ki te 6.

$$g=\frac{39±33}{12}$$

Nā, me whakaoti te whārite g=\frac{39±33}{12} ina he tāpiri te ±. Tāpiri 39 ki te 33.

$$g=\frac{72}{12}$$

Whakawehe 72 ki te 12.

$$g=6$$

Nā, me whakaoti te whārite g=\frac{39±33}{12} ina he tango te ±. Tango 33 mai i 39.

$$g=\frac{6}{12}$$

Whakahekea te hautanga \frac{6}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$g=\frac{1}{2}$$

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 6 mō te x_{1} me te \frac{1}{2} mō te x_{2}.

$$6g^{2}-39g+18=6\left(g-6\right)\left(g-\frac{1}{2}\right)$$

Tango \frac{1}{2} mai i g mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$6g^{2}-39g+18=6\left(g-6\right)\times \frac{2g-1}{2}$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 6 me te 2.

$$6g^{2}-39g+18=3\left(g-6\right)\left(2g-1\right)$$

Aromātai

$$3\left(g-6\right)\left(2g-1\right)$$