Whakaoti i te 3-a-a^2

$$3 - a - a ^ { 2 }$$

Tauwehe

$$-\left(a-\frac{-\sqrt{13}-1}{2}\right)\left(a-\frac{\sqrt{13}-1}{2}\right)$$

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.

$$-a^{2}-a+3=0$$

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.

$$a=\frac{-\left(-1\right)±\sqrt{1-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$a=\frac{-\left(-1\right)±\sqrt{1+4\times 3}}{2\left(-1\right)}$$

Whakareatia 4 ki te 3.

$$a=\frac{-\left(-1\right)±\sqrt{1+12}}{2\left(-1\right)}$$

Tāpiri 1 ki te 12.

$$a=\frac{-\left(-1\right)±\sqrt{13}}{2\left(-1\right)}$$

Ko te tauaro o -1 ko 1.

$$a=\frac{1±\sqrt{13}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$a=\frac{1±\sqrt{13}}{-2}$$

Nā, me whakaoti te whārite a=\frac{1±\sqrt{13}}{-2} ina he tāpiri te ±. Tāpiri 1 ki te \sqrt{13}.

$$a=\frac{\sqrt{13}+1}{-2}$$

Whakawehe 1+\sqrt{13} ki te -2.

$$a=\frac{-\sqrt{13}-1}{2}$$

Nā, me whakaoti te whārite a=\frac{1±\sqrt{13}}{-2} ina he tango te ±. Tango \sqrt{13} mai i 1.

$$a=\frac{1-\sqrt{13}}{-2}$$

Whakawehe 1-\sqrt{13} ki te -2.

$$a=\frac{\sqrt{13}-1}{2}$$

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{13}}{2} mō te x_{1} me te \frac{-1+\sqrt{13}}{2} mō te x_{2}.

$$-a^{2}-a+3=-\left(a-\frac{-\sqrt{13}-1}{2}\right)\left(a-\frac{\sqrt{13}-1}{2}\right)$$

Aromātai

$$3-a-a^{2}$$