Whakaoti i te y^2-12y-27

$$y ^ { 2 } - 12 y - 27$$

Tauwehe

$$\left(y-\left(6-3\sqrt{7}\right)\right)\left(y-\left(3\sqrt{7}+6\right)\right)$$

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.

$$y^{2}-12y-27=0$$

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.

$$y=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\left(-27\right)}}{2}$$

Pūrua -12.

$$y=\frac{-\left(-12\right)±\sqrt{144-4\left(-27\right)}}{2}$$

Whakareatia -4 ki te -27.

$$y=\frac{-\left(-12\right)±\sqrt{144+108}}{2}$$

Tāpiri 144 ki te 108.

$$y=\frac{-\left(-12\right)±\sqrt{252}}{2}$$

Tuhia te pūtakerua o te 252.

$$y=\frac{-\left(-12\right)±6\sqrt{7}}{2}$$

Ko te tauaro o -12 ko 12.

$$y=\frac{12±6\sqrt{7}}{2}$$

Nā, me whakaoti te whārite y=\frac{12±6\sqrt{7}}{2} ina he tāpiri te ±. Tāpiri 12 ki te 6\sqrt{7}.

$$y=\frac{6\sqrt{7}+12}{2}$$

Whakawehe 12+6\sqrt{7} ki te 2.

$$y=3\sqrt{7}+6$$

Nā, me whakaoti te whārite y=\frac{12±6\sqrt{7}}{2} ina he tango te ±. Tango 6\sqrt{7} mai i 12.

$$y=\frac{12-6\sqrt{7}}{2}$$

Whakawehe 12-6\sqrt{7} ki te 2.

$$y=6-3\sqrt{7}$$

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+3\sqrt{7} mō te x_{1} me te 6-3\sqrt{7} mō te x_{2}.

$$y^{2}-12y-27=\left(y-\left(3\sqrt{7}+6\right)\right)\left(y-\left(6-3\sqrt{7}\right)\right)$$

Aromātai

$$y^{2}-12y-27$$