Whakaoti i te 4x^2-20x+5

$$4 { x }^{ 2 } -20x+5$$

Tauwehe

$$4\left(x-\left(\frac{5}{2}-\sqrt{5}\right)\right)\left(x-\left(\sqrt{5}+\frac{5}{2}\right)\right)$$

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.

$$4x^{2}-20x+5=0$$

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.

$$x=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}-4\times 4\times 5}}{2\times 4}$$

Pūrua -20.

$$x=\frac{-\left(-20\right)±\sqrt{400-4\times 4\times 5}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-\left(-20\right)±\sqrt{400-16\times 5}}{2\times 4}$$

Whakareatia -16 ki te 5.

$$x=\frac{-\left(-20\right)±\sqrt{400-80}}{2\times 4}$$

Tāpiri 400 ki te -80.

$$x=\frac{-\left(-20\right)±\sqrt{320}}{2\times 4}$$

Tuhia te pūtakerua o te 320.

$$x=\frac{-\left(-20\right)±8\sqrt{5}}{2\times 4}$$

Ko te tauaro o -20 ko 20.

$$x=\frac{20±8\sqrt{5}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{20±8\sqrt{5}}{8}$$

Nā, me whakaoti te whārite x=\frac{20±8\sqrt{5}}{8} ina he tāpiri te ±. Tāpiri 20 ki te 8\sqrt{5}.

$$x=\frac{8\sqrt{5}+20}{8}$$

Whakawehe 20+8\sqrt{5} ki te 8.

$$x=\sqrt{5}+\frac{5}{2}$$

Nā, me whakaoti te whārite x=\frac{20±8\sqrt{5}}{8} ina he tango te ±. Tango 8\sqrt{5} mai i 20.

$$x=\frac{20-8\sqrt{5}}{8}$$

Whakawehe 20-8\sqrt{5} ki te 8.

$$x=\frac{5}{2}-\sqrt{5}$$

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

$$4x^{2}-20x+5=4\left(x-\left(\sqrt{5}+\frac{5}{2}\right)\right)\left(x-\left(\frac{5}{2}-\sqrt{5}\right)\right)$$

Aromātai

$$4x^{2}-20x+5$$