Whakaoti i te 6y^2-21y+12

$$6 y ^ { 2 } - 21 y + 12$$

Tauwehe

$$6\left(y-\frac{7-\sqrt{17}}{4}\right)\left(y-\frac{\sqrt{17}+7}{4}\right)$$

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.

$$6y^{2}-21y+12=0$$

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.

$$y=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}-4\times 6\times 12}}{2\times 6}$$

Pūrua -21.

$$y=\frac{-\left(-21\right)±\sqrt{441-4\times 6\times 12}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$y=\frac{-\left(-21\right)±\sqrt{441-24\times 12}}{2\times 6}$$

Whakareatia -24 ki te 12.

$$y=\frac{-\left(-21\right)±\sqrt{441-288}}{2\times 6}$$

Tāpiri 441 ki te -288.

$$y=\frac{-\left(-21\right)±\sqrt{153}}{2\times 6}$$

Tuhia te pūtakerua o te 153.

$$y=\frac{-\left(-21\right)±3\sqrt{17}}{2\times 6}$$

Ko te tauaro o -21 ko 21.

$$y=\frac{21±3\sqrt{17}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$y=\frac{21±3\sqrt{17}}{12}$$

Nā, me whakaoti te whārite y=\frac{21±3\sqrt{17}}{12} ina he tāpiri te ±. Tāpiri 21 ki te 3\sqrt{17}.

$$y=\frac{3\sqrt{17}+21}{12}$$

Whakawehe 21+3\sqrt{17} ki te 12.

$$y=\frac{\sqrt{17}+7}{4}$$

Nā, me whakaoti te whārite y=\frac{21±3\sqrt{17}}{12} ina he tango te ±. Tango 3\sqrt{17} mai i 21.

$$y=\frac{21-3\sqrt{17}}{12}$$

Whakawehe 21-3\sqrt{17} ki te 12.

$$y=\frac{7-\sqrt{17}}{4}$$

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 \frac{7+\sqrt{17}}{4} mō te x_{1} me te \frac{7-\sqrt{17}}{4} mō te x_{2}.

$$6y^{2}-21y+12=6\left(y-\frac{\sqrt{17}+7}{4}\right)\left(y-\frac{7-\sqrt{17}}{4}\right)$$

Aromātai

$$6y^{2}-21y+12$$