Whakaoti i te f(x)=3x-x^2

$$f ( x ) = 3 x - x ^ { 2 }$$

Tauwehe

$$x\left(3-x\right)$$

Ngā Upane Otinga

Tauwehea te x.

$$x\left(3-x\right)$$

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.

$$-x^{2}+3x=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 3^{2}.

$$x=\frac{-3±3}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-3±3}{-2}$$

Nā, me whakaoti te whārite x=\frac{-3±3}{-2} ina he tāpiri te ±. Tāpiri -3 ki te 3.

$$x=\frac{0}{-2}$$

Whakawehe 0 ki te -2.

$$x=0$$

Nā, me whakaoti te whārite x=\frac{-3±3}{-2} ina he tango te ±. Tango 3 mai i -3.

$$x=-\frac{6}{-2}$$

Whakawehe -6 ki te -2.

$$x=3$$

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 0 mō te x_{1} me te 3 mō te x_{2}.

$$-x^{2}+3x=-x\left(x-3\right)$$

Aromātai

$$x\left(3-x\right)$$