Whakaoti i te y^2-9y-18

$${ y }^{ 2 } -9y-18$$

Tauwehe

$$\left(y-\frac{9-3\sqrt{17}}{2}\right)\left(y-\frac{3\sqrt{17}+9}{2}\right)$$

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.

$$y^{2}-9y-18=0$$

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.

$$y=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\left(-18\right)}}{2}$$

Pūrua -9.

$$y=\frac{-\left(-9\right)±\sqrt{81-4\left(-18\right)}}{2}$$

Whakareatia -4 ki te -18.

$$y=\frac{-\left(-9\right)±\sqrt{81+72}}{2}$$

Tāpiri 81 ki te 72.

$$y=\frac{-\left(-9\right)±\sqrt{153}}{2}$$

Tuhia te pūtakerua o te 153.

$$y=\frac{-\left(-9\right)±3\sqrt{17}}{2}$$

Ko te tauaro o -9 ko 9.

$$y=\frac{9±3\sqrt{17}}{2}$$

Nā, me whakaoti te whārite y=\frac{9±3\sqrt{17}}{2} ina he tāpiri te ±. Tāpiri 9 ki te 3\sqrt{17}.

$$y=\frac{3\sqrt{17}+9}{2}$$

Nā, me whakaoti te whārite y=\frac{9±3\sqrt{17}}{2} ina he tango te ±. Tango 3\sqrt{17} mai i 9.

$$y=\frac{9-3\sqrt{17}}{2}$$

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{9+3\sqrt{17}}{2} mō te x_{1} me te \frac{9-3\sqrt{17}}{2} mō te x_{2}.

$$y^{2}-9y-18=\left(y-\frac{3\sqrt{17}+9}{2}\right)\left(y-\frac{9-3\sqrt{17}}{2}\right)$$

Aromātai

$$y^{2}-9y-18$$