Whakaoti i te 6x^2+8x+1

$$6 x ^ { 2 } + 8 x + 1$$

Tauwehe

$$6\left(x-\left(-\frac{\sqrt{10}}{6}-\frac{2}{3}\right)\right)\left(x-\left(\frac{\sqrt{10}}{6}-\frac{2}{3}\right)\right)$$

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.

$$6x^{2}+8x+1=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\times 6}}{2\times 6}$$

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\times 6}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-8±\sqrt{64-24}}{2\times 6}$$

Tāpiri 64 ki te -24.

$$x=\frac{-8±\sqrt{40}}{2\times 6}$$

Tuhia te pūtakerua o te 40.

$$x=\frac{-8±2\sqrt{10}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{-8±2\sqrt{10}}{12}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{10}}{12} ina he tāpiri te ±. Tāpiri -8 ki te 2\sqrt{10}.

$$x=\frac{2\sqrt{10}-8}{12}$$

Whakawehe -8+2\sqrt{10} ki te 12.

$$x=\frac{\sqrt{10}}{6}-\frac{2}{3}$$

Nā, me whakaoti te whārite x=\frac{-8±2\sqrt{10}}{12} ina he tango te ±. Tango 2\sqrt{10} mai i -8.

$$x=\frac{-2\sqrt{10}-8}{12}$$

Whakawehe -8-2\sqrt{10} ki te 12.

$$x=-\frac{\sqrt{10}}{6}-\frac{2}{3}$$

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{2}{3}+\frac{\sqrt{10}}{6} mō te x_{1} me te -\frac{2}{3}-\frac{\sqrt{10}}{6} mō te x_{2}.

$$6x^{2}+8x+1=6\left(x-\left(\frac{\sqrt{10}}{6}-\frac{2}{3}\right)\right)\left(x-\left(-\frac{\sqrt{10}}{6}-\frac{2}{3}\right)\right)$$

Aromātai

$$6x^{2}+8x+1$$