Whakaoti i te a^2+6a+9a^2-9

$$a ^ { 2 } + 6 a + 9 a ^ { 2 } - 9$$

Tauwehe

$$10\left(a-\frac{-3\sqrt{11}-3}{10}\right)\left(a-\frac{3\sqrt{11}-3}{10}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Pahekotia te a^{2} me 9a^{2}, ka 10a^{2}.

$$factor(10a^{2}+6a-9)$$

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.

$$10a^{2}+6a-9=0$$

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.

$$a=\frac{-6±\sqrt{6^{2}-4\times 10\left(-9\right)}}{2\times 10}$$

Pūrua 6.

$$a=\frac{-6±\sqrt{36-4\times 10\left(-9\right)}}{2\times 10}$$

Whakareatia -4 ki te 10.

$$a=\frac{-6±\sqrt{36-40\left(-9\right)}}{2\times 10}$$

Whakareatia -40 ki te -9.

$$a=\frac{-6±\sqrt{36+360}}{2\times 10}$$

Tāpiri 36 ki te 360.

$$a=\frac{-6±\sqrt{396}}{2\times 10}$$

Tuhia te pūtakerua o te 396.

$$a=\frac{-6±6\sqrt{11}}{2\times 10}$$

Whakareatia 2 ki te 10.

$$a=\frac{-6±6\sqrt{11}}{20}$$

Nā, me whakaoti te whārite a=\frac{-6±6\sqrt{11}}{20} ina he tāpiri te ±. Tāpiri -6 ki te 6\sqrt{11}.

$$a=\frac{6\sqrt{11}-6}{20}$$

Whakawehe -6+6\sqrt{11} ki te 20.

$$a=\frac{3\sqrt{11}-3}{10}$$

Nā, me whakaoti te whārite a=\frac{-6±6\sqrt{11}}{20} ina he tango te ±. Tango 6\sqrt{11} mai i -6.

$$a=\frac{-6\sqrt{11}-6}{20}$$

Whakawehe -6-6\sqrt{11} ki te 20.

$$a=\frac{-3\sqrt{11}-3}{10}$$

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+3\sqrt{11}}{10} mō te x_{1} me te \frac{-3-3\sqrt{11}}{10} mō te x_{2}.

$$10a^{2}+6a-9=10\left(a-\frac{3\sqrt{11}-3}{10}\right)\left(a-\frac{-3\sqrt{11}-3}{10}\right)$$

Aromātai

$$10a^{2}+6a-9$$

Ngā Upane Otinga

Pahekotia te a^{2} me 9a^{2}, ka 10a^{2}.

$$10a^{2}+6a-9$$