Whakaoti i te x^2-10x-48

$${ x }^{ 2 } -10x-48$$

Tauwehe

$$\left(x-\left(5-\sqrt{73}\right)\right)\left(x-\left(\sqrt{73}+5\right)\right)$$

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.

$$x^{2}-10x-48=0$$

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.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\left(-48\right)}}{2}$$

Pūrua -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\left(-48\right)}}{2}$$

Whakareatia -4 ki te -48.

$$x=\frac{-\left(-10\right)±\sqrt{100+192}}{2}$$

Tāpiri 100 ki te 192.

$$x=\frac{-\left(-10\right)±\sqrt{292}}{2}$$

Tuhia te pūtakerua o te 292.

$$x=\frac{-\left(-10\right)±2\sqrt{73}}{2}$$

Ko te tauaro o -10 ko 10.

$$x=\frac{10±2\sqrt{73}}{2}$$

Nā, me whakaoti te whārite x=\frac{10±2\sqrt{73}}{2} ina he tāpiri te ±. Tāpiri 10 ki te 2\sqrt{73}.

$$x=\frac{2\sqrt{73}+10}{2}$$

Whakawehe 10+2\sqrt{73} ki te 2.

$$x=\sqrt{73}+5$$

Nā, me whakaoti te whārite x=\frac{10±2\sqrt{73}}{2} ina he tango te ±. Tango 2\sqrt{73} mai i 10.

$$x=\frac{10-2\sqrt{73}}{2}$$

Whakawehe 10-2\sqrt{73} ki te 2.

$$x=5-\sqrt{73}$$

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 5+\sqrt{73} mō te x_{1} me te 5-\sqrt{73} mō te x_{2}.

$$x^{2}-10x-48=\left(x-\left(\sqrt{73}+5\right)\right)\left(x-\left(5-\sqrt{73}\right)\right)$$

Aromātai

$$x^{2}-10x-48$$