Whakaoti i te 9x^2+18x+1

$$9 x ^ { 2 } + 18 x + 1$$

Tauwehe

$$9\left(x-\left(-\frac{2\sqrt{2}}{3}-1\right)\right)\left(x-\left(\frac{2\sqrt{2}}{3}-1\right)\right)$$

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.

$$9x^{2}+18x+1=0$$

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.

$$x=\frac{-18±\sqrt{18^{2}-4\times 9}}{2\times 9}$$

Pūrua 18.

$$x=\frac{-18±\sqrt{324-4\times 9}}{2\times 9}$$

Whakareatia -4 ki te 9.

$$x=\frac{-18±\sqrt{324-36}}{2\times 9}$$

Tāpiri 324 ki te -36.

$$x=\frac{-18±\sqrt{288}}{2\times 9}$$

Tuhia te pūtakerua o te 288.

$$x=\frac{-18±12\sqrt{2}}{2\times 9}$$

Whakareatia 2 ki te 9.

$$x=\frac{-18±12\sqrt{2}}{18}$$

Nā, me whakaoti te whārite x=\frac{-18±12\sqrt{2}}{18} ina he tāpiri te ±. Tāpiri -18 ki te 12\sqrt{2}.

$$x=\frac{12\sqrt{2}-18}{18}$$

Whakawehe -18+12\sqrt{2} ki te 18.

$$x=\frac{2\sqrt{2}}{3}-1$$

Nā, me whakaoti te whārite x=\frac{-18±12\sqrt{2}}{18} ina he tango te ±. Tango 12\sqrt{2} mai i -18.

$$x=\frac{-12\sqrt{2}-18}{18}$$

Whakawehe -18-12\sqrt{2} ki te 18.

$$x=-\frac{2\sqrt{2}}{3}-1$$

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

$$9x^{2}+18x+1=9\left(x-\left(\frac{2\sqrt{2}}{3}-1\right)\right)\left(x-\left(-\frac{2\sqrt{2}}{3}-1\right)\right)$$

Aromātai

$$9x^{2}+18x+1$$