Whakaoti i te x^2-110x+50

$$x ^ { 2 } - 110 x + 50$$

Tauwehe

$$\left(x-\left(55-5\sqrt{119}\right)\right)\left(x-\left(5\sqrt{119}+55\right)\right)$$

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.

$$x^{2}-110x+50=0$$

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.

$$x=\frac{-\left(-110\right)±\sqrt{\left(-110\right)^{2}-4\times 50}}{2}$$

Pūrua -110.

$$x=\frac{-\left(-110\right)±\sqrt{12100-4\times 50}}{2}$$

Whakareatia -4 ki te 50.

$$x=\frac{-\left(-110\right)±\sqrt{12100-200}}{2}$$

Tāpiri 12100 ki te -200.

$$x=\frac{-\left(-110\right)±\sqrt{11900}}{2}$$

Tuhia te pūtakerua o te 11900.

$$x=\frac{-\left(-110\right)±10\sqrt{119}}{2}$$

Ko te tauaro o -110 ko 110.

$$x=\frac{110±10\sqrt{119}}{2}$$

Nā, me whakaoti te whārite x=\frac{110±10\sqrt{119}}{2} ina he tāpiri te ±. Tāpiri 110 ki te 10\sqrt{119}.

$$x=\frac{10\sqrt{119}+110}{2}$$

Whakawehe 110+10\sqrt{119} ki te 2.

$$x=5\sqrt{119}+55$$

Nā, me whakaoti te whārite x=\frac{110±10\sqrt{119}}{2} ina he tango te ±. Tango 10\sqrt{119} mai i 110.

$$x=\frac{110-10\sqrt{119}}{2}$$

Whakawehe 110-10\sqrt{119} ki te 2.

$$x=55-5\sqrt{119}$$

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 55+5\sqrt{119} mō te x_{1} me te 55-5\sqrt{119} mō te x_{2}.

$$x^{2}-110x+50=\left(x-\left(5\sqrt{119}+55\right)\right)\left(x-\left(55-5\sqrt{119}\right)\right)$$

Aromātai

$$x^{2}-110x+50$$