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

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

Aromātai

$$10w^{2}-4w-3$$

Ngā Upane Otinga

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

$$10w^{2}-w-5-3w+2$$

Pahekotia te -w me -3w, ka -4w.

$$10w^{2}-4w-5+2$$

Tāpirihia te -5 ki te 2, ka -3.

$$10w^{2}-4w-3$$

Tauwehe

$$10\left(w-\left(-\frac{\sqrt{34}}{10}+\frac{1}{5}\right)\right)\left(w-\left(\frac{\sqrt{34}}{10}+\frac{1}{5}\right)\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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

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

Pahekotia te -w me -3w, ka -4w.

$$factor(10w^{2}-4w-5+2)$$

Tāpirihia te -5 ki te 2, ka -3.

$$factor(10w^{2}-4w-3)$$

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.

$$10w^{2}-4w-3=0$$

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.

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

Pūrua -4.

$$w=\frac{-\left(-4\right)±\sqrt{16-4\times 10\left(-3\right)}}{2\times 10}$$

Whakareatia -4 ki te 10.

$$w=\frac{-\left(-4\right)±\sqrt{16-40\left(-3\right)}}{2\times 10}$$

Whakareatia -40 ki te -3.

$$w=\frac{-\left(-4\right)±\sqrt{16+120}}{2\times 10}$$

Tāpiri 16 ki te 120.

$$w=\frac{-\left(-4\right)±\sqrt{136}}{2\times 10}$$

Tuhia te pūtakerua o te 136.

$$w=\frac{-\left(-4\right)±2\sqrt{34}}{2\times 10}$$

Ko te tauaro o -4 ko 4.

$$w=\frac{4±2\sqrt{34}}{2\times 10}$$

Whakareatia 2 ki te 10.

$$w=\frac{4±2\sqrt{34}}{20}$$

Nā, me whakaoti te whārite w=\frac{4±2\sqrt{34}}{20} ina he tāpiri te ±. Tāpiri 4 ki te 2\sqrt{34}.

$$w=\frac{2\sqrt{34}+4}{20}$$

Whakawehe 4+2\sqrt{34} ki te 20.

$$w=\frac{\sqrt{34}}{10}+\frac{1}{5}$$

Nā, me whakaoti te whārite w=\frac{4±2\sqrt{34}}{20} ina he tango te ±. Tango 2\sqrt{34} mai i 4.

$$w=\frac{4-2\sqrt{34}}{20}$$

Whakawehe 4-2\sqrt{34} ki te 20.

$$w=-\frac{\sqrt{34}}{10}+\frac{1}{5}$$

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 \frac{1}{5}+\frac{\sqrt{34}}{10} mō te x_{1} me te \frac{1}{5}-\frac{\sqrt{34}}{10} mō te x_{2}.

$$10w^{2}-4w-3=10\left(w-\left(\frac{\sqrt{34}}{10}+\frac{1}{5}\right)\right)\left(w-\left(-\frac{\sqrt{34}}{10}+\frac{1}{5}\right)\right)$$