Whakaoti i te 5x^2-7x+x-3

$$5 x ^ { 2 } - 7 x + x - 3$$

Tauwehe

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te -7x me x, ka -6x.

$$factor(5x^{2}-6x-3)$$

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.

$$5x^{2}-6x-3=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\times 5\left(-3\right)}}{2\times 5}$$

Pūrua -6.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\times 5\left(-3\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$x=\frac{-\left(-6\right)±\sqrt{36-20\left(-3\right)}}{2\times 5}$$

Whakareatia -20 ki te -3.

$$x=\frac{-\left(-6\right)±\sqrt{36+60}}{2\times 5}$$

Tāpiri 36 ki te 60.

$$x=\frac{-\left(-6\right)±\sqrt{96}}{2\times 5}$$

Tuhia te pūtakerua o te 96.

$$x=\frac{-\left(-6\right)±4\sqrt{6}}{2\times 5}$$

Ko te tauaro o -6 ko 6.

$$x=\frac{6±4\sqrt{6}}{2\times 5}$$

Whakareatia 2 ki te 5.

$$x=\frac{6±4\sqrt{6}}{10}$$

Nā, me whakaoti te whārite x=\frac{6±4\sqrt{6}}{10} ina he tāpiri te ±. Tāpiri 6 ki te 4\sqrt{6}.

$$x=\frac{4\sqrt{6}+6}{10}$$

Whakawehe 6+4\sqrt{6} ki te 10.

$$x=\frac{2\sqrt{6}+3}{5}$$

Nā, me whakaoti te whārite x=\frac{6±4\sqrt{6}}{10} ina he tango te ±. Tango 4\sqrt{6} mai i 6.

$$x=\frac{6-4\sqrt{6}}{10}$$

Whakawehe 6-4\sqrt{6} ki te 10.

$$x=\frac{3-2\sqrt{6}}{5}$$

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{3+2\sqrt{6}}{5} mō te x_{1} me te \frac{3-2\sqrt{6}}{5} mō te x_{2}.

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

Aromātai

$$5x^{2}-6x-3$$

Ngā Upane Otinga

Pahekotia te -7x me x, ka -6x.

$$5x^{2}-6x-3$$