Whakaoti i te 3x^2-36x+104

$$3 { x }^{ 2 } -36x+104$$

Tauwehe

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

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.

$$3x^{2}-36x+104=0$$

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.

$$x=\frac{-\left(-36\right)±\sqrt{\left(-36\right)^{2}-4\times 3\times 104}}{2\times 3}$$

Pūrua -36.

$$x=\frac{-\left(-36\right)±\sqrt{1296-4\times 3\times 104}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-36\right)±\sqrt{1296-12\times 104}}{2\times 3}$$

Whakareatia -12 ki te 104.

$$x=\frac{-\left(-36\right)±\sqrt{1296-1248}}{2\times 3}$$

Tāpiri 1296 ki te -1248.

$$x=\frac{-\left(-36\right)±\sqrt{48}}{2\times 3}$$

Tuhia te pūtakerua o te 48.

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

Ko te tauaro o -36 ko 36.

$$x=\frac{36±4\sqrt{3}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{36±4\sqrt{3}}{6}$$

Nā, me whakaoti te whārite x=\frac{36±4\sqrt{3}}{6} ina he tāpiri te ±. Tāpiri 36 ki te 4\sqrt{3}.

$$x=\frac{4\sqrt{3}+36}{6}$$

Whakawehe 36+4\sqrt{3} ki te 6.

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

Nā, me whakaoti te whārite x=\frac{36±4\sqrt{3}}{6} ina he tango te ±. Tango 4\sqrt{3} mai i 36.

$$x=\frac{36-4\sqrt{3}}{6}$$

Whakawehe 36-4\sqrt{3} ki te 6.

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

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

$$3x^{2}-36x+104=3\left(x-\left(\frac{2\sqrt{3}}{3}+6\right)\right)\left(x-\left(-\frac{2\sqrt{3}}{3}+6\right)\right)$$

Aromātai

$$3x^{2}-36x+104$$