Whakaoti i te =-10+10x-x^2

$$= - 10 + 10 x - x ^ { 2 }$$

Tauwehe

$$-\left(x-\left(5-\sqrt{15}\right)\right)\left(x-\left(\sqrt{15}+5\right)\right)$$

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.

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

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.

$$x=\frac{-10±\sqrt{10^{2}-4\left(-1\right)\left(-10\right)}}{2\left(-1\right)}$$

Pūrua 10.

$$x=\frac{-10±\sqrt{100-4\left(-1\right)\left(-10\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-10±\sqrt{100+4\left(-10\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -10.

$$x=\frac{-10±\sqrt{100-40}}{2\left(-1\right)}$$

Tāpiri 100 ki te -40.

$$x=\frac{-10±\sqrt{60}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 60.

$$x=\frac{-10±2\sqrt{15}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-10±2\sqrt{15}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-10±2\sqrt{15}}{-2} ina he tāpiri te ±. Tāpiri -10 ki te 2\sqrt{15}.

$$x=\frac{2\sqrt{15}-10}{-2}$$

Whakawehe -10+2\sqrt{15} ki te -2.

$$x=5-\sqrt{15}$$

Nā, me whakaoti te whārite x=\frac{-10±2\sqrt{15}}{-2} ina he tango te ±. Tango 2\sqrt{15} mai i -10.

$$x=\frac{-2\sqrt{15}-10}{-2}$$

Whakawehe -10-2\sqrt{15} ki te -2.

$$x=\sqrt{15}+5$$

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 5-\sqrt{15} mō te x_{1} me te 5+\sqrt{15} mō te x_{2}.

$$-x^{2}+10x-10=-\left(x-\left(5-\sqrt{15}\right)\right)\left(x-\left(\sqrt{15}+5\right)\right)$$

Aromātai

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