Whakaoti i te 5x^2-12x+5

$$5 { x }^{ 2 } -12x+5$$

Tauwehe

$$5\left(x-\frac{6-\sqrt{11}}{5}\right)\left(x-\frac{\sqrt{11}+6}{5}\right)$$

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.

$$5x^{2}-12x+5=0$$

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.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 5\times 5}}{2\times 5}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 5\times 5}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-12\right)±\sqrt{144-20\times 5}}{2\times 5}$$

Whakareatia -20 ki te 5.

$$x=\frac{-\left(-12\right)±\sqrt{144-100}}{2\times 5}$$

Tāpiri 144 ki te -100.

$$x=\frac{-\left(-12\right)±\sqrt{44}}{2\times 5}$$

Tuhia te pūtakerua o te 44.

$$x=\frac{-\left(-12\right)±2\sqrt{11}}{2\times 5}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±2\sqrt{11}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{12±2\sqrt{11}}{10}$$

Nā, me whakaoti te whārite x=\frac{12±2\sqrt{11}}{10} ina he tāpiri te ±. Tāpiri 12 ki te 2\sqrt{11}.

$$x=\frac{2\sqrt{11}+12}{10}$$

Whakawehe 12+2\sqrt{11} ki te 10.

$$x=\frac{\sqrt{11}+6}{5}$$

Nā, me whakaoti te whārite x=\frac{12±2\sqrt{11}}{10} ina he tango te ±. Tango 2\sqrt{11} mai i 12.

$$x=\frac{12-2\sqrt{11}}{10}$$

Whakawehe 12-2\sqrt{11} ki te 10.

$$x=\frac{6-\sqrt{11}}{5}$$

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{6+\sqrt{11}}{5} mō te x_{1} me te \frac{6-\sqrt{11}}{5} mō te x_{2}.

$$5x^{2}-12x+5=5\left(x-\frac{\sqrt{11}+6}{5}\right)\left(x-\frac{6-\sqrt{11}}{5}\right)$$

Aromātai

$$5x^{2}-12x+5$$