Whakaoti i te 4a^2-9-12a

$$4 a ^ { 2 } - 9 - 12 a$$

Tauwehe

$$4\left(a-\frac{3-3\sqrt{2}}{2}\right)\left(a-\frac{3\sqrt{2}+3}{2}\right)$$

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.

$$4a^{2}-12a-9=0$$

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.

$$a=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 4\left(-9\right)}}{2\times 4}$$

Pūrua -12.

$$a=\frac{-\left(-12\right)±\sqrt{144-4\times 4\left(-9\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$a=\frac{-\left(-12\right)±\sqrt{144-16\left(-9\right)}}{2\times 4}$$

Whakareatia -16 ki te -9.

$$a=\frac{-\left(-12\right)±\sqrt{144+144}}{2\times 4}$$

Tāpiri 144 ki te 144.

$$a=\frac{-\left(-12\right)±\sqrt{288}}{2\times 4}$$

Tuhia te pūtakerua o te 288.

$$a=\frac{-\left(-12\right)±12\sqrt{2}}{2\times 4}$$

Ko te tauaro o -12 ko 12.

$$a=\frac{12±12\sqrt{2}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$a=\frac{12±12\sqrt{2}}{8}$$

Nā, me whakaoti te whārite a=\frac{12±12\sqrt{2}}{8} ina he tāpiri te ±. Tāpiri 12 ki te 12\sqrt{2}.

$$a=\frac{12\sqrt{2}+12}{8}$$

Whakawehe 12+12\sqrt{2} ki te 8.

$$a=\frac{3\sqrt{2}+3}{2}$$

Nā, me whakaoti te whārite a=\frac{12±12\sqrt{2}}{8} ina he tango te ±. Tango 12\sqrt{2} mai i 12.

$$a=\frac{12-12\sqrt{2}}{8}$$

Whakawehe 12-12\sqrt{2} ki te 8.

$$a=\frac{3-3\sqrt{2}}{2}$$

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

$$4a^{2}-12a-9=4\left(a-\frac{3\sqrt{2}+3}{2}\right)\left(a-\frac{3-3\sqrt{2}}{2}\right)$$

Aromātai

$$4a^{2}-12a-9$$