Whakaoti i te b^2-26b+89

$$b ^ { 2 } - 26 b + 89$$

Tauwehe

$$\left(b-\left(13-4\sqrt{5}\right)\right)\left(b-\left(4\sqrt{5}+13\right)\right)$$

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.

$$b^{2}-26b+89=0$$

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.

$$b=\frac{-\left(-26\right)±\sqrt{\left(-26\right)^{2}-4\times 89}}{2}$$

Pūrua -26.

$$b=\frac{-\left(-26\right)±\sqrt{676-4\times 89}}{2}$$

Whakareatia -4 ki te 89.

$$b=\frac{-\left(-26\right)±\sqrt{676-356}}{2}$$

Tāpiri 676 ki te -356.

$$b=\frac{-\left(-26\right)±\sqrt{320}}{2}$$

Tuhia te pūtakerua o te 320.

$$b=\frac{-\left(-26\right)±8\sqrt{5}}{2}$$

Ko te tauaro o -26 ko 26.

$$b=\frac{26±8\sqrt{5}}{2}$$

Nā, me whakaoti te whārite b=\frac{26±8\sqrt{5}}{2} ina he tāpiri te ±. Tāpiri 26 ki te 8\sqrt{5}.

$$b=\frac{8\sqrt{5}+26}{2}$$

Whakawehe 26+8\sqrt{5} ki te 2.

$$b=4\sqrt{5}+13$$

Nā, me whakaoti te whārite b=\frac{26±8\sqrt{5}}{2} ina he tango te ±. Tango 8\sqrt{5} mai i 26.

$$b=\frac{26-8\sqrt{5}}{2}$$

Whakawehe 26-8\sqrt{5} ki te 2.

$$b=13-4\sqrt{5}$$

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 13+4\sqrt{5} mō te x_{1} me te 13-4\sqrt{5} mō te x_{2}.

$$b^{2}-26b+89=\left(b-\left(4\sqrt{5}+13\right)\right)\left(b-\left(13-4\sqrt{5}\right)\right)$$

Aromātai

$$b^{2}-26b+89$$