Whakaoti i te (-y^2-2y+3)+(-7y^2+4)

$$( - y ^ { 2 } - 2 y + 3 ) + ( - 7 y ^ { 2 } + 4 )$$

Aromātai

$$7-2y-8y^{2}$$

Ngā Upane Otinga

Tāpirihia te 3 ki te 4, ka 7.

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

Pahekotia te -y^{2} me -7y^{2}, ka -8y^{2}.

$$-8y^{2}-2y+7$$

Tauwehe

$$-8\left(y-\frac{-\sqrt{57}-1}{8}\right)\left(y-\frac{\sqrt{57}-1}{8}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 3 ki te 4, ka 7.

$$factor(-y^{2}-2y+7-7y^{2})$$

Pahekotia te -y^{2} me -7y^{2}, ka -8y^{2}.

$$factor(-8y^{2}-2y+7)$$

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.

$$-8y^{2}-2y+7=0$$

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.

$$y=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-8\right)\times 7}}{2\left(-8\right)}$$

Pūrua -2.

$$y=\frac{-\left(-2\right)±\sqrt{4-4\left(-8\right)\times 7}}{2\left(-8\right)}$$

Whakareatia -4 ki te -8.

$$y=\frac{-\left(-2\right)±\sqrt{4+32\times 7}}{2\left(-8\right)}$$

Whakareatia 32 ki te 7.

$$y=\frac{-\left(-2\right)±\sqrt{4+224}}{2\left(-8\right)}$$

Tāpiri 4 ki te 224.

$$y=\frac{-\left(-2\right)±\sqrt{228}}{2\left(-8\right)}$$

Tuhia te pūtakerua o te 228.

$$y=\frac{-\left(-2\right)±2\sqrt{57}}{2\left(-8\right)}$$

Ko te tauaro o -2 ko 2.

$$y=\frac{2±2\sqrt{57}}{2\left(-8\right)}$$

Whakareatia 2 ki te -8.

$$y=\frac{2±2\sqrt{57}}{-16}$$

Nā, me whakaoti te whārite y=\frac{2±2\sqrt{57}}{-16} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{57}.

$$y=\frac{2\sqrt{57}+2}{-16}$$

Whakawehe 2+2\sqrt{57} ki te -16.

$$y=\frac{-\sqrt{57}-1}{8}$$

Nā, me whakaoti te whārite y=\frac{2±2\sqrt{57}}{-16} ina he tango te ±. Tango 2\sqrt{57} mai i 2.

$$y=\frac{2-2\sqrt{57}}{-16}$$

Whakawehe 2-2\sqrt{57} ki te -16.

$$y=\frac{\sqrt{57}-1}{8}$$

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{-1-\sqrt{57}}{8} mō te x_{1} me te \frac{-1+\sqrt{57}}{8} mō te x_{2}.

$$-8y^{2}-2y+7=-8\left(y-\frac{-\sqrt{57}-1}{8}\right)\left(y-\frac{\sqrt{57}-1}{8}\right)$$