Whakaoti i te 16x^2-24x-11

$$16 { x }^{ 2 } -24x-11$$

Tauwehe

$$16\left(x-\left(-\frac{\sqrt{5}}{2}+\frac{3}{4}\right)\right)\left(x-\left(\frac{\sqrt{5}}{2}+\frac{3}{4}\right)\right)$$

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.

$$16x^{2}-24x-11=0$$

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.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 16\left(-11\right)}}{2\times 16}$$

Pūrua -24.

$$x=\frac{-\left(-24\right)±\sqrt{576-4\times 16\left(-11\right)}}{2\times 16}$$

Whakareatia -4 ki te 16.

$$x=\frac{-\left(-24\right)±\sqrt{576-64\left(-11\right)}}{2\times 16}$$

Whakareatia -64 ki te -11.

$$x=\frac{-\left(-24\right)±\sqrt{576+704}}{2\times 16}$$

Tāpiri 576 ki te 704.

$$x=\frac{-\left(-24\right)±\sqrt{1280}}{2\times 16}$$

Tuhia te pūtakerua o te 1280.

$$x=\frac{-\left(-24\right)±16\sqrt{5}}{2\times 16}$$

Ko te tauaro o -24 ko 24.

$$x=\frac{24±16\sqrt{5}}{2\times 16}$$

Whakareatia 2 ki te 16.

$$x=\frac{24±16\sqrt{5}}{32}$$

Nā, me whakaoti te whārite x=\frac{24±16\sqrt{5}}{32} ina he tāpiri te ±. Tāpiri 24 ki te 16\sqrt{5}.

$$x=\frac{16\sqrt{5}+24}{32}$$

Whakawehe 24+16\sqrt{5} ki te 32.

$$x=\frac{\sqrt{5}}{2}+\frac{3}{4}$$

Nā, me whakaoti te whārite x=\frac{24±16\sqrt{5}}{32} ina he tango te ±. Tango 16\sqrt{5} mai i 24.

$$x=\frac{24-16\sqrt{5}}{32}$$

Whakawehe 24-16\sqrt{5} ki te 32.

$$x=-\frac{\sqrt{5}}{2}+\frac{3}{4}$$

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{3}{4}+\frac{\sqrt{5}}{2} mō te x_{1} me te \frac{3}{4}-\frac{\sqrt{5}}{2} mō te x_{2}.

$$16x^{2}-24x-11=16\left(x-\left(\frac{\sqrt{5}}{2}+\frac{3}{4}\right)\right)\left(x-\left(-\frac{\sqrt{5}}{2}+\frac{3}{4}\right)\right)$$

Aromātai

$$16x^{2}-24x-11$$