Whakaoti i te 6u^2+5u-6

$$6 u ^ { 2 } + 5 u - 6$$

Tauwehe

$$\left(3u-2\right)\left(2u+3\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 6u^{2}+au+bu-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=6\left(-6\right)=-36$$

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. 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.

$$-1+36=35 -2+18=16 -3+12=9 -4+9=5 -6+6=0$$

Ko te otinga te takirua ka hoatu i te tapeke 5.

$$a=-4 b=9$$

Tuhia anō te 6u^{2}+5u-6 hei \left(6u^{2}-4u\right)+\left(9u-6\right).

$$\left(6u^{2}-4u\right)+\left(9u-6\right)$$

Tauwehea te 2u i te tuatahi me te 3 i te rōpū tuarua.

$$2u\left(3u-2\right)+3\left(3u-2\right)$$

Whakatauwehea atu te kīanga pātahi 3u-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(3u-2\right)\left(2u+3\right)$$

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.

$$6u^{2}+5u-6=0$$

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.

$$u=\frac{-5±\sqrt{5^{2}-4\times 6\left(-6\right)}}{2\times 6}$$

Pūrua 5.

$$u=\frac{-5±\sqrt{25-4\times 6\left(-6\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$u=\frac{-5±\sqrt{25-24\left(-6\right)}}{2\times 6}$$

Whakareatia -24 ki te -6.

$$u=\frac{-5±\sqrt{25+144}}{2\times 6}$$

Tāpiri 25 ki te 144.

$$u=\frac{-5±\sqrt{169}}{2\times 6}$$

Tuhia te pūtakerua o te 169.

$$u=\frac{-5±13}{2\times 6}$$

Whakareatia 2 ki te 6.

$$u=\frac{-5±13}{12}$$

Nā, me whakaoti te whārite u=\frac{-5±13}{12} ina he tāpiri te ±. Tāpiri -5 ki te 13.

$$u=\frac{8}{12}$$

Whakahekea te hautanga \frac{8}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$u=\frac{2}{3}$$

Nā, me whakaoti te whārite u=\frac{-5±13}{12} ina he tango te ±. Tango 13 mai i -5.

$$u=-\frac{18}{12}$$

Whakahekea te hautanga \frac{-18}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$u=-\frac{3}{2}$$

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 \frac{2}{3} mō te x_{1} me te -\frac{3}{2} mō te x_{2}.

$$6u^{2}+5u-6=6\left(u-\frac{2}{3}\right)\left(u-\left(-\frac{3}{2}\right)\right)$$

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

$$6u^{2}+5u-6=6\left(u-\frac{2}{3}\right)\left(u+\frac{3}{2}\right)$$

Tango \frac{2}{3} mai i u 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.

$$6u^{2}+5u-6=6\times \frac{3u-2}{3}\left(u+\frac{3}{2}\right)$$

Tāpiri \frac{3}{2} ki te u 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.

$$6u^{2}+5u-6=6\times \frac{3u-2}{3}\times \frac{2u+3}{2}$$

Whakareatia \frac{3u-2}{3} ki te \frac{2u+3}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$6u^{2}+5u-6=6\times \frac{\left(3u-2\right)\left(2u+3\right)}{3\times 2}$$

Whakareatia 3 ki te 2.

$$6u^{2}+5u-6=6\times \frac{\left(3u-2\right)\left(2u+3\right)}{6}$$

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

$$6u^{2}+5u-6=\left(3u-2\right)\left(2u+3\right)$$

Aromātai

$$\left(3u-2\right)\left(2u+3\right)$$