Whakaoti i te 3x^2-7x-3=?

$$3 x ^ { 2 } - 7 x - 3 = ?$$

Tauwehe

$$3\left(x-\frac{7-\sqrt{85}}{6}\right)\left(x-\frac{\sqrt{85}+7}{6}\right)$$

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.

$$3x^{2}-7x-3=0$$

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.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 3\left(-3\right)}}{2\times 3}$$

Pūrua -7.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\times 3\left(-3\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-7\right)±\sqrt{49-12\left(-3\right)}}{2\times 3}$$

Whakareatia -12 ki te -3.

$$x=\frac{-\left(-7\right)±\sqrt{49+36}}{2\times 3}$$

Tāpiri 49 ki te 36.

$$x=\frac{-\left(-7\right)±\sqrt{85}}{2\times 3}$$

Ko te tauaro o -7 ko 7.

$$x=\frac{7±\sqrt{85}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{7±\sqrt{85}}{6}$$

Nā, me whakaoti te whārite x=\frac{7±\sqrt{85}}{6} ina he tāpiri te ±. Tāpiri 7 ki te \sqrt{85}.

$$x=\frac{\sqrt{85}+7}{6}$$

Nā, me whakaoti te whārite x=\frac{7±\sqrt{85}}{6} ina he tango te ±. Tango \sqrt{85} mai i 7.

$$x=\frac{7-\sqrt{85}}{6}$$

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{7+\sqrt{85}}{6} mō te x_{1} me te \frac{7-\sqrt{85}}{6} mō te x_{2}.

$$3x^{2}-7x-3=3\left(x-\frac{\sqrt{85}+7}{6}\right)\left(x-\frac{7-\sqrt{85}}{6}\right)$$

Aromātai

$$3x^{2}-7x-3$$