Whakaoti i te x^2+6x+2=?

$$x ^ { 2 } + 6 x + 2 = ?$$

Tauwehe

$$\left(x-\left(-\sqrt{7}-3\right)\right)\left(x-\left(\sqrt{7}-3\right)\right)$$

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.

$$x^{2}+6x+2=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 2}}{2}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\times 2}}{2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-6±\sqrt{36-8}}{2}$$

Tāpiri 36 ki te -8.

$$x=\frac{-6±\sqrt{28}}{2}$$

Tuhia te pūtakerua o te 28.

$$x=\frac{-6±2\sqrt{7}}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{7}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{7}.

$$x=\frac{2\sqrt{7}-6}{2}$$

Whakawehe -6+2\sqrt{7} ki te 2.

$$x=\sqrt{7}-3$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{7}}{2} ina he tango te ±. Tango 2\sqrt{7} mai i -6.

$$x=\frac{-2\sqrt{7}-6}{2}$$

Whakawehe -6-2\sqrt{7} ki te 2.

$$x=-\sqrt{7}-3$$

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 -3+\sqrt{7} mō te x_{1} me te -3-\sqrt{7} mō te x_{2}.

$$x^{2}+6x+2=\left(x-\left(\sqrt{7}-3\right)\right)\left(x-\left(-\sqrt{7}-3\right)\right)$$

Aromātai

$$x^{2}+6x+2$$