Whakaoti i te 3y^2-10y-24div3y-4

$$3 { y }^{ 2 } -10y-24 \div 3y-4$$

Aromātai

$$3y^{2}-18y-4$$

Ngā Upane Otinga

Whakawehea te 24 ki te 3, kia riro ko 8.

$$3y^{2}-10y-8y-4$$

Pahekotia te -10y me -8y, ka -18y.

$$3y^{2}-18y-4$$

Tauwehe

$$3\left(y-\left(-\frac{\sqrt{93}}{3}+3\right)\right)\left(y-\left(\frac{\sqrt{93}}{3}+3\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea te 24 ki te 3, kia riro ko 8.

$$factor(3y^{2}-10y-8y-4)$$

Pahekotia te -10y me -8y, ka -18y.

$$factor(3y^{2}-18y-4)$$

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.

$$3y^{2}-18y-4=0$$

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.

$$y=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}-4\times 3\left(-4\right)}}{2\times 3}$$

Pūrua -18.

$$y=\frac{-\left(-18\right)±\sqrt{324-4\times 3\left(-4\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$y=\frac{-\left(-18\right)±\sqrt{324-12\left(-4\right)}}{2\times 3}$$

Whakareatia -12 ki te -4.

$$y=\frac{-\left(-18\right)±\sqrt{324+48}}{2\times 3}$$

Tāpiri 324 ki te 48.

$$y=\frac{-\left(-18\right)±\sqrt{372}}{2\times 3}$$

Tuhia te pūtakerua o te 372.

$$y=\frac{-\left(-18\right)±2\sqrt{93}}{2\times 3}$$

Ko te tauaro o -18 ko 18.

$$y=\frac{18±2\sqrt{93}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$y=\frac{18±2\sqrt{93}}{6}$$

Nā, me whakaoti te whārite y=\frac{18±2\sqrt{93}}{6} ina he tāpiri te ±. Tāpiri 18 ki te 2\sqrt{93}.

$$y=\frac{2\sqrt{93}+18}{6}$$

Whakawehe 18+2\sqrt{93} ki te 6.

$$y=\frac{\sqrt{93}}{3}+3$$

Nā, me whakaoti te whārite y=\frac{18±2\sqrt{93}}{6} ina he tango te ±. Tango 2\sqrt{93} mai i 18.

$$y=\frac{18-2\sqrt{93}}{6}$$

Whakawehe 18-2\sqrt{93} ki te 6.

$$y=-\frac{\sqrt{93}}{3}+3$$

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 3+\frac{\sqrt{93}}{3} mō te x_{1} me te 3-\frac{\sqrt{93}}{3} mō te x_{2}.

$$3y^{2}-18y-4=3\left(y-\left(\frac{\sqrt{93}}{3}+3\right)\right)\left(y-\left(-\frac{\sqrt{93}}{3}+3\right)\right)$$