Whakaoti i te 8x^2-2x-8

$$8 x ^ { 2 } - 2 x - 8$$

Tauwehe

$$8\left(x-\frac{1-\sqrt{65}}{8}\right)\left(x-\frac{\sqrt{65}+1}{8}\right)$$

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.

$$8x^{2}-2x-8=0$$

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.

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

Pūrua -2.

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

Whakareatia -4 ki te 8.

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

Whakareatia -32 ki te -8.

$$x=\frac{-\left(-2\right)±\sqrt{4+256}}{2\times 8}$$

Tāpiri 4 ki te 256.

$$x=\frac{-\left(-2\right)±\sqrt{260}}{2\times 8}$$

Tuhia te pūtakerua o te 260.

$$x=\frac{-\left(-2\right)±2\sqrt{65}}{2\times 8}$$

Ko te tauaro o -2 ko 2.

$$x=\frac{2±2\sqrt{65}}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{2±2\sqrt{65}}{16}$$

Nā, me whakaoti te whārite x=\frac{2±2\sqrt{65}}{16} ina he tāpiri te ±. Tāpiri 2 ki te 2\sqrt{65}.

$$x=\frac{2\sqrt{65}+2}{16}$$

Whakawehe 2+2\sqrt{65} ki te 16.

$$x=\frac{\sqrt{65}+1}{8}$$

Nā, me whakaoti te whārite x=\frac{2±2\sqrt{65}}{16} ina he tango te ±. Tango 2\sqrt{65} mai i 2.

$$x=\frac{2-2\sqrt{65}}{16}$$

Whakawehe 2-2\sqrt{65} ki te 16.

$$x=\frac{1-\sqrt{65}}{8}$$

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{65}}{8} mō te x_{1} me te \frac{1-\sqrt{65}}{8} mō te x_{2}.

$$8x^{2}-2x-8=8\left(x-\frac{\sqrt{65}+1}{8}\right)\left(x-\frac{1-\sqrt{65}}{8}\right)$$

Aromātai

$$8x^{2}-2x-8$$