Whakaoti i te 6u^2+24u-36

$$6 u ^ { 2 } + 24 u - 36$$

Tauwehe

$$6\left(u-\left(-\sqrt{10}-2\right)\right)\left(u-\left(\sqrt{10}-2\right)\right)$$

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.

$$6u^{2}+24u-36=0$$

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.

$$u=\frac{-24±\sqrt{24^{2}-4\times 6\left(-36\right)}}{2\times 6}$$

Pūrua 24.

$$u=\frac{-24±\sqrt{576-4\times 6\left(-36\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$u=\frac{-24±\sqrt{576-24\left(-36\right)}}{2\times 6}$$

Whakareatia -24 ki te -36.

$$u=\frac{-24±\sqrt{576+864}}{2\times 6}$$

Tāpiri 576 ki te 864.

$$u=\frac{-24±\sqrt{1440}}{2\times 6}$$

Tuhia te pūtakerua o te 1440.

$$u=\frac{-24±12\sqrt{10}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$u=\frac{-24±12\sqrt{10}}{12}$$

Nā, me whakaoti te whārite u=\frac{-24±12\sqrt{10}}{12} ina he tāpiri te ±. Tāpiri -24 ki te 12\sqrt{10}.

$$u=\frac{12\sqrt{10}-24}{12}$$

Whakawehe -24+12\sqrt{10} ki te 12.

$$u=\sqrt{10}-2$$

Nā, me whakaoti te whārite u=\frac{-24±12\sqrt{10}}{12} ina he tango te ±. Tango 12\sqrt{10} mai i -24.

$$u=\frac{-12\sqrt{10}-24}{12}$$

Whakawehe -24-12\sqrt{10} ki te 12.

$$u=-\sqrt{10}-2$$

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 -2+\sqrt{10} mō te x_{1} me te -2-\sqrt{10} mō te x_{2}.

$$6u^{2}+24u-36=6\left(u-\left(\sqrt{10}-2\right)\right)\left(u-\left(-\sqrt{10}-2\right)\right)$$

Aromātai

$$6\left(u^{2}+4u-6\right)$$