Whakaoti i te (4v^2+5)+(6v^2-3v-7)

$$( 4 v ^ { 2 } + 5 ) + ( 6 v ^ { 2 } - 3 v - 7 )$$

Aromātai

$$10v^{2}-3v-2$$

Ngā Upane Otinga

Pahekotia te 4v^{2} me 6v^{2}, ka 10v^{2}.

$$10v^{2}+5-3v-7$$

Tangohia te 7 i te 5, ka -2.

$$10v^{2}-2-3v$$

Tauwehe

$$10\left(v-\frac{3-\sqrt{89}}{20}\right)\left(v-\frac{\sqrt{89}+3}{20}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te 4v^{2} me 6v^{2}, ka 10v^{2}.

$$factor(10v^{2}+5-3v-7)$$

Tangohia te 7 i te 5, ka -2.

$$factor(10v^{2}-2-3v)$$

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.

$$10v^{2}-3v-2=0$$

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.

$$v=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 10\left(-2\right)}}{2\times 10}$$

Pūrua -3.

$$v=\frac{-\left(-3\right)±\sqrt{9-4\times 10\left(-2\right)}}{2\times 10}$$

Whakareatia -4 ki te 10.

$$v=\frac{-\left(-3\right)±\sqrt{9-40\left(-2\right)}}{2\times 10}$$

Whakareatia -40 ki te -2.

$$v=\frac{-\left(-3\right)±\sqrt{9+80}}{2\times 10}$$

Tāpiri 9 ki te 80.

$$v=\frac{-\left(-3\right)±\sqrt{89}}{2\times 10}$$

Ko te tauaro o -3 ko 3.

$$v=\frac{3±\sqrt{89}}{2\times 10}$$

Whakareatia 2 ki te 10.

$$v=\frac{3±\sqrt{89}}{20}$$

Nā, me whakaoti te whārite v=\frac{3±\sqrt{89}}{20} ina he tāpiri te ±. Tāpiri 3 ki te \sqrt{89}.

$$v=\frac{\sqrt{89}+3}{20}$$

Nā, me whakaoti te whārite v=\frac{3±\sqrt{89}}{20} ina he tango te ±. Tango \sqrt{89} mai i 3.

$$v=\frac{3-\sqrt{89}}{20}$$

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{3+\sqrt{89}}{20} mō te x_{1} me te \frac{3-\sqrt{89}}{20} mō te x_{2}.

$$10v^{2}-3v-2=10\left(v-\frac{\sqrt{89}+3}{20}\right)\left(v-\frac{3-\sqrt{89}}{20}\right)$$