Whakaoti i te 3d^2-3d-2

$$3 d ^ { 2 } - 3 d - 2$$

Tauwehe

$$3\left(d-\left(-\frac{\sqrt{33}}{6}+\frac{1}{2}\right)\right)\left(d-\left(\frac{\sqrt{33}}{6}+\frac{1}{2}\right)\right)$$

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.

$$3d^{2}-3d-2=0$$

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.

$$d=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 3\left(-2\right)}}{2\times 3}$$

Pūrua -3.

$$d=\frac{-\left(-3\right)±\sqrt{9-4\times 3\left(-2\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$d=\frac{-\left(-3\right)±\sqrt{9-12\left(-2\right)}}{2\times 3}$$

Whakareatia -12 ki te -2.

$$d=\frac{-\left(-3\right)±\sqrt{9+24}}{2\times 3}$$

Tāpiri 9 ki te 24.

$$d=\frac{-\left(-3\right)±\sqrt{33}}{2\times 3}$$

Ko te tauaro o -3 ko 3.

$$d=\frac{3±\sqrt{33}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$d=\frac{3±\sqrt{33}}{6}$$

Nā, me whakaoti te whārite d=\frac{3±\sqrt{33}}{6} ina he tāpiri te ±. Tāpiri 3 ki te \sqrt{33}.

$$d=\frac{\sqrt{33}+3}{6}$$

Whakawehe 3+\sqrt{33} ki te 6.

$$d=\frac{\sqrt{33}}{6}+\frac{1}{2}$$

Nā, me whakaoti te whārite d=\frac{3±\sqrt{33}}{6} ina he tango te ±. Tango \sqrt{33} mai i 3.

$$d=\frac{3-\sqrt{33}}{6}$$

Whakawehe 3-\sqrt{33} ki te 6.

$$d=-\frac{\sqrt{33}}{6}+\frac{1}{2}$$

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 \frac{1}{2}+\frac{\sqrt{33}}{6} mō te x_{1} me te \frac{1}{2}-\frac{\sqrt{33}}{6} mō te x_{2}.

$$3d^{2}-3d-2=3\left(d-\left(\frac{\sqrt{33}}{6}+\frac{1}{2}\right)\right)\left(d-\left(-\frac{\sqrt{33}}{6}+\frac{1}{2}\right)\right)$$

Aromātai

$$3d^{2}-3d-2$$