Whakaoti i te 2y^2+7y-1)

$$2 y ^ { 2 } + 7 y - 1 )$$

Tauwehe

$$2\left(y-\frac{-\sqrt{57}-7}{4}\right)\left(y-\frac{\sqrt{57}-7}{4}\right)$$

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.

$$2y^{2}+7y-1=0$$

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.

$$y=\frac{-7±\sqrt{7^{2}-4\times 2\left(-1\right)}}{2\times 2}$$

Pūrua 7.

$$y=\frac{-7±\sqrt{49-4\times 2\left(-1\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$y=\frac{-7±\sqrt{49-8\left(-1\right)}}{2\times 2}$$

Whakareatia -8 ki te -1.

$$y=\frac{-7±\sqrt{49+8}}{2\times 2}$$

Tāpiri 49 ki te 8.

$$y=\frac{-7±\sqrt{57}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$y=\frac{-7±\sqrt{57}}{4}$$

Nā, me whakaoti te whārite y=\frac{-7±\sqrt{57}}{4} ina he tāpiri te ±. Tāpiri -7 ki te \sqrt{57}.

$$y=\frac{\sqrt{57}-7}{4}$$

Nā, me whakaoti te whārite y=\frac{-7±\sqrt{57}}{4} ina he tango te ±. Tango \sqrt{57} mai i -7.

$$y=\frac{-\sqrt{57}-7}{4}$$

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{57}}{4} mō te x_{1} me te \frac{-7-\sqrt{57}}{4} mō te x_{2}.

$$2y^{2}+7y-1=2\left(y-\frac{\sqrt{57}-7}{4}\right)\left(y-\frac{-\sqrt{57}-7}{4}\right)$$

Aromātai

$$2y^{2}+7y-1$$