Whakaoti i te (t^2-6t+2)+(5t^2-t-8)

$$( t ^ { 2 } - 6 t + 2 ) + ( 5 t ^ { 2 } - t - 8 )$$

Aromātai

$$6t^{2}-7t-6$$

Ngā Upane Otinga

Pahekotia te t^{2} me 5t^{2}, ka 6t^{2}.

$$6t^{2}-6t+2-t-8$$

Pahekotia te -6t me -t, ka -7t.

$$6t^{2}-7t+2-8$$

Tangohia te 8 i te 2, ka -6.

$$6t^{2}-7t-6$$

Tauwehe

$$6\left(t-\frac{7-\sqrt{193}}{12}\right)\left(t-\frac{\sqrt{193}+7}{12}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te t^{2} me 5t^{2}, ka 6t^{2}.

$$factor(6t^{2}-6t+2-t-8)$$

Pahekotia te -6t me -t, ka -7t.

$$factor(6t^{2}-7t+2-8)$$

Tangohia te 8 i te 2, ka -6.

$$factor(6t^{2}-7t-6)$$

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.

$$6t^{2}-7t-6=0$$

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.

$$t=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 6\left(-6\right)}}{2\times 6}$$

Pūrua -7.

$$t=\frac{-\left(-7\right)±\sqrt{49-4\times 6\left(-6\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$t=\frac{-\left(-7\right)±\sqrt{49-24\left(-6\right)}}{2\times 6}$$

Whakareatia -24 ki te -6.

$$t=\frac{-\left(-7\right)±\sqrt{49+144}}{2\times 6}$$

Tāpiri 49 ki te 144.

$$t=\frac{-\left(-7\right)±\sqrt{193}}{2\times 6}$$

Ko te tauaro o -7 ko 7.

$$t=\frac{7±\sqrt{193}}{2\times 6}$$

Whakareatia 2 ki te 6.

$$t=\frac{7±\sqrt{193}}{12}$$

Nā, me whakaoti te whārite t=\frac{7±\sqrt{193}}{12} ina he tāpiri te ±. Tāpiri 7 ki te \sqrt{193}.

$$t=\frac{\sqrt{193}+7}{12}$$

Nā, me whakaoti te whārite t=\frac{7±\sqrt{193}}{12} ina he tango te ±. Tango \sqrt{193} mai i 7.

$$t=\frac{7-\sqrt{193}}{12}$$

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{7+\sqrt{193}}{12} mō te x_{1} me te \frac{7-\sqrt{193}}{12} mō te x_{2}.

$$6t^{2}-7t-6=6\left(t-\frac{\sqrt{193}+7}{12}\right)\left(t-\frac{7-\sqrt{193}}{12}\right)$$