Whakaoti i te 8x^2-6x-4

$$8 x ^ { 2 } - 6 x - 4$$

Tauwehe

$$8\left(x-\frac{3-\sqrt{41}}{8}\right)\left(x-\frac{\sqrt{41}+3}{8}\right)$$

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.

$$8x^{2}-6x-4=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 8\left(-4\right)}}{2\times 8}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 8\left(-4\right)}}{2\times 8}$$

Whakareatia -4 ki te 8.

$$x=\frac{-\left(-6\right)±\sqrt{36-32\left(-4\right)}}{2\times 8}$$

Whakareatia -32 ki te -4.

$$x=\frac{-\left(-6\right)±\sqrt{36+128}}{2\times 8}$$

Tāpiri 36 ki te 128.

$$x=\frac{-\left(-6\right)±\sqrt{164}}{2\times 8}$$

Tuhia te pūtakerua o te 164.

$$x=\frac{-\left(-6\right)±2\sqrt{41}}{2\times 8}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±2\sqrt{41}}{2\times 8}$$

Whakareatia 2 ki te 8.

$$x=\frac{6±2\sqrt{41}}{16}$$

Nā, me whakaoti te whārite x=\frac{6±2\sqrt{41}}{16} ina he tāpiri te ±. Tāpiri 6 ki te 2\sqrt{41}.

$$x=\frac{2\sqrt{41}+6}{16}$$

Whakawehe 6+2\sqrt{41} ki te 16.

$$x=\frac{\sqrt{41}+3}{8}$$

Nā, me whakaoti te whārite x=\frac{6±2\sqrt{41}}{16} ina he tango te ±. Tango 2\sqrt{41} mai i 6.

$$x=\frac{6-2\sqrt{41}}{16}$$

Whakawehe 6-2\sqrt{41} ki te 16.

$$x=\frac{3-\sqrt{41}}{8}$$

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+\sqrt{41}}{8} mō te x_{1} me te \frac{3-\sqrt{41}}{8} mō te x_{2}.

$$8x^{2}-6x-4=8\left(x-\frac{\sqrt{41}+3}{8}\right)\left(x-\frac{3-\sqrt{41}}{8}\right)$$

Aromātai

$$8x^{2}-6x-4$$