Whakaoti i te 4a^2-4a-1=

$$4 a ^ { 2 } - 4 a - 1 =$$

Tauwehe

$$4\left(a-\frac{1-\sqrt{2}}{2}\right)\left(a-\frac{\sqrt{2}+1}{2}\right)$$

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.

$$4a^{2}-4a-1=0$$

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.

$$a=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 4\left(-1\right)}}{2\times 4}$$

Pūrua -4.

$$a=\frac{-\left(-4\right)±\sqrt{16-4\times 4\left(-1\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$a=\frac{-\left(-4\right)±\sqrt{16-16\left(-1\right)}}{2\times 4}$$

Whakareatia -16 ki te -1.

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

Tāpiri 16 ki te 16.

$$a=\frac{-\left(-4\right)±\sqrt{32}}{2\times 4}$$

Tuhia te pūtakerua o te 32.

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

Ko te tauaro o -4 ko 4.

$$a=\frac{4±4\sqrt{2}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$a=\frac{4±4\sqrt{2}}{8}$$

Nā, me whakaoti te whārite a=\frac{4±4\sqrt{2}}{8} ina he tāpiri te ±. Tāpiri 4 ki te 4\sqrt{2}.

$$a=\frac{4\sqrt{2}+4}{8}$$

Whakawehe 4+4\sqrt{2} ki te 8.

$$a=\frac{\sqrt{2}+1}{2}$$

Nā, me whakaoti te whārite a=\frac{4±4\sqrt{2}}{8} ina he tango te ±. Tango 4\sqrt{2} mai i 4.

$$a=\frac{4-4\sqrt{2}}{8}$$

Whakawehe 4-4\sqrt{2} ki te 8.

$$a=\frac{1-\sqrt{2}}{2}$$

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

$$4a^{2}-4a-1=4\left(a-\frac{\sqrt{2}+1}{2}\right)\left(a-\frac{1-\sqrt{2}}{2}\right)$$

Aromātai

$$4a^{2}-4a-1$$