Whakaoti i te 3x^2-x-5

$$3 x ^ { 2 } - x - 5$$

Tauwehe

$$3\left(x-\frac{1-\sqrt{61}}{6}\right)\left(x-\frac{\sqrt{61}+1}{6}\right)$$

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.

$$3x^{2}-x-5=0$$

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.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 3\left(-5\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-1\right)±\sqrt{1-12\left(-5\right)}}{2\times 3}$$

Whakareatia -12 ki te -5.

$$x=\frac{-\left(-1\right)±\sqrt{1+60}}{2\times 3}$$

Tāpiri 1 ki te 60.

$$x=\frac{-\left(-1\right)±\sqrt{61}}{2\times 3}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±\sqrt{61}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{1±\sqrt{61}}{6}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{61}}{6} ina he tāpiri te ±. Tāpiri 1 ki te \sqrt{61}.

$$x=\frac{\sqrt{61}+1}{6}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{61}}{6} ina he tango te ±. Tango \sqrt{61} mai i 1.

$$x=\frac{1-\sqrt{61}}{6}$$

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{1+\sqrt{61}}{6} mō te x_{1} me te \frac{1-\sqrt{61}}{6} mō te x_{2}.

$$3x^{2}-x-5=3\left(x-\frac{\sqrt{61}+1}{6}\right)\left(x-\frac{1-\sqrt{61}}{6}\right)$$

Aromātai

$$3x^{2}-x-5$$