Whakaoti i te x^2-42x+45=

$${ x }^{ 2 } -42x+45=$$

Tauwehe

$$\left(x-\left(21-6\sqrt{11}\right)\right)\left(x-\left(6\sqrt{11}+21\right)\right)$$

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.

$$x^{2}-42x+45=0$$

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.

$$x=\frac{-\left(-42\right)±\sqrt{\left(-42\right)^{2}-4\times 45}}{2}$$

Pūrua -42.

$$x=\frac{-\left(-42\right)±\sqrt{1764-4\times 45}}{2}$$

Whakareatia -4 ki te 45.

$$x=\frac{-\left(-42\right)±\sqrt{1764-180}}{2}$$

Tāpiri 1764 ki te -180.

$$x=\frac{-\left(-42\right)±\sqrt{1584}}{2}$$

Tuhia te pūtakerua o te 1584.

$$x=\frac{-\left(-42\right)±12\sqrt{11}}{2}$$

Ko te tauaro o -42 ko 42.

$$x=\frac{42±12\sqrt{11}}{2}$$

Nā, me whakaoti te whārite x=\frac{42±12\sqrt{11}}{2} ina he tāpiri te ±. Tāpiri 42 ki te 12\sqrt{11}.

$$x=\frac{12\sqrt{11}+42}{2}$$

Whakawehe 42+12\sqrt{11} ki te 2.

$$x=6\sqrt{11}+21$$

Nā, me whakaoti te whārite x=\frac{42±12\sqrt{11}}{2} ina he tango te ±. Tango 12\sqrt{11} mai i 42.

$$x=\frac{42-12\sqrt{11}}{2}$$

Whakawehe 42-12\sqrt{11} ki te 2.

$$x=21-6\sqrt{11}$$

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 21+6\sqrt{11} mō te x_{1} me te 21-6\sqrt{11} mō te x_{2}.

$$x^{2}-42x+45=\left(x-\left(6\sqrt{11}+21\right)\right)\left(x-\left(21-6\sqrt{11}\right)\right)$$

Aromātai

$$x^{2}-42x+45$$