Whakaoti i te f(x)=2x^2-8x+7

$$f ( x ) = 2 x ^ { 2 } - 8 x + 7$$

Tauwehe

$$2\left(x-\left(-\frac{\sqrt{2}}{2}+2\right)\right)\left(x-\left(\frac{\sqrt{2}}{2}+2\right)\right)$$

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.

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

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.

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

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 2\times 7}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-8\right)±\sqrt{64-8\times 7}}{2\times 2}$$

Whakareatia -8 ki te 7.

$$x=\frac{-\left(-8\right)±\sqrt{64-56}}{2\times 2}$$

Tāpiri 64 ki te -56.

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

Tuhia te pūtakerua o te 8.

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

Ko te tauaro o -8 ko 8.

$$x=\frac{8±2\sqrt{2}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{8±2\sqrt{2}}{4}$$

Nā, me whakaoti te whārite x=\frac{8±2\sqrt{2}}{4} ina he tāpiri te ±. Tāpiri 8 ki te 2\sqrt{2}.

$$x=\frac{2\sqrt{2}+8}{4}$$

Whakawehe 2\sqrt{2}+8 ki te 4.

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

Nā, me whakaoti te whārite x=\frac{8±2\sqrt{2}}{4} ina he tango te ±. Tango 2\sqrt{2} mai i 8.

$$x=\frac{8-2\sqrt{2}}{4}$$

Whakawehe 8-2\sqrt{2} ki te 4.

$$x=-\frac{\sqrt{2}}{2}+2$$

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

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

Aromātai

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