Whakaoti i te 2x^2+4x-1

$$2 { x }^{ 2 } +4x-1$$

Tauwehe

$$2\left(x-\left(-\frac{\sqrt{6}}{2}-1\right)\right)\left(x-\left(\frac{\sqrt{6}}{2}-1\right)\right)$$

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.

$$2x^{2}+4x-1=0$$

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.

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

Pūrua 4.

$$x=\frac{-4±\sqrt{16-4\times 2\left(-1\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-4±\sqrt{16-8\left(-1\right)}}{2\times 2}$$

Whakareatia -8 ki te -1.

$$x=\frac{-4±\sqrt{16+8}}{2\times 2}$$

Tāpiri 16 ki te 8.

$$x=\frac{-4±\sqrt{24}}{2\times 2}$$

Tuhia te pūtakerua o te 24.

$$x=\frac{-4±2\sqrt{6}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-4±2\sqrt{6}}{4}$$

Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{6}}{4} ina he tāpiri te ±. Tāpiri -4 ki te 2\sqrt{6}.

$$x=\frac{2\sqrt{6}-4}{4}$$

Whakawehe -4+2\sqrt{6} ki te 4.

$$x=\frac{\sqrt{6}}{2}-1$$

Nā, me whakaoti te whārite x=\frac{-4±2\sqrt{6}}{4} ina he tango te ±. Tango 2\sqrt{6} mai i -4.

$$x=\frac{-2\sqrt{6}-4}{4}$$

Whakawehe -4-2\sqrt{6} ki te 4.

$$x=-\frac{\sqrt{6}}{2}-1$$

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

$$2x^{2}+4x-1=2\left(x-\left(\frac{\sqrt{6}}{2}-1\right)\right)\left(x-\left(-\frac{\sqrt{6}}{2}-1\right)\right)$$

Aromātai

$$2x^{2}+4x-1$$