Whakaoti i te X^2+6X-2

$$X ^ { 2 } + 6 X - 2$$

Tauwehe

$$\left(X-\left(-\sqrt{11}-3\right)\right)\left(X-\left(\sqrt{11}-3\right)\right)$$

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.

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

Pūrua 6.

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

Whakareatia -4 ki te -2.

$$X=\frac{-6±\sqrt{36+8}}{2}$$

Tāpiri 36 ki te 8.

$$X=\frac{-6±\sqrt{44}}{2}$$

Tuhia te pūtakerua o te 44.

$$X=\frac{-6±2\sqrt{11}}{2}$$

Nā, me whakaoti te whārite X=\frac{-6±2\sqrt{11}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{11}.

$$X=\frac{2\sqrt{11}-6}{2}$$

Whakawehe -6+2\sqrt{11} ki te 2.

$$X=\sqrt{11}-3$$

Nā, me whakaoti te whārite X=\frac{-6±2\sqrt{11}}{2} ina he tango te ±. Tango 2\sqrt{11} mai i -6.

$$X=\frac{-2\sqrt{11}-6}{2}$$

Whakawehe -6-2\sqrt{11} ki te 2.

$$X=-\sqrt{11}-3$$

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{11} mō te x_{1} me te -3-\sqrt{11} mō te x_{2}.

$$X^{2}+6X-2=\left(X-\left(\sqrt{11}-3\right)\right)\left(X-\left(-\sqrt{11}-3\right)\right)$$

Aromātai

$$X^{2}+6X-2$$