Whakaoti i te 65y^2-23y-10

$$65 y ^ { 2 } - 23 y - 10$$

Tauwehe

$$65\left(y-\frac{23-\sqrt{3129}}{130}\right)\left(y-\frac{\sqrt{3129}+23}{130}\right)$$

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.

$$65y^{2}-23y-10=0$$

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.

$$y=\frac{-\left(-23\right)±\sqrt{\left(-23\right)^{2}-4\times 65\left(-10\right)}}{2\times 65}$$

Pūrua -23.

$$y=\frac{-\left(-23\right)±\sqrt{529-4\times 65\left(-10\right)}}{2\times 65}$$

Whakareatia -4 ki te 65.

$$y=\frac{-\left(-23\right)±\sqrt{529-260\left(-10\right)}}{2\times 65}$$

Whakareatia -260 ki te -10.

$$y=\frac{-\left(-23\right)±\sqrt{529+2600}}{2\times 65}$$

Tāpiri 529 ki te 2600.

$$y=\frac{-\left(-23\right)±\sqrt{3129}}{2\times 65}$$

Ko te tauaro o -23 ko 23.

$$y=\frac{23±\sqrt{3129}}{2\times 65}$$

Whakareatia 2 ki te 65.

$$y=\frac{23±\sqrt{3129}}{130}$$

Nā, me whakaoti te whārite y=\frac{23±\sqrt{3129}}{130} ina he tāpiri te ±. Tāpiri 23 ki te \sqrt{3129}.

$$y=\frac{\sqrt{3129}+23}{130}$$

Nā, me whakaoti te whārite y=\frac{23±\sqrt{3129}}{130} ina he tango te ±. Tango \sqrt{3129} mai i 23.

$$y=\frac{23-\sqrt{3129}}{130}$$

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{23+\sqrt{3129}}{130} mō te x_{1} me te \frac{23-\sqrt{3129}}{130} mō te x_{2}.

$$65y^{2}-23y-10=65\left(y-\frac{\sqrt{3129}+23}{130}\right)\left(y-\frac{23-\sqrt{3129}}{130}\right)$$

Aromātai

$$65y^{2}-23y-10$$