Whakaoti i te 01375x^3-11707x^2+52978x-23667

$$01375 { x }^{ 3 } -11707 { x }^{ 2 } +52978x-23667$$

Aromātai

$$-11707x^{2}+52978x-23667$$

Ngā Upane Otinga

Whakareatia te 0 ki te 1375, ka 0.

$$0x^{3}-11707x^{2}+52978x-23667$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$0-11707x^{2}+52978x-23667$$

Tangohia te 23667 i te 0, ka -23667.

$$-23667-11707x^{2}+52978x$$

Tauwehe

$$-11707\left(x-\frac{26489-4\sqrt{26537347}}{11707}\right)\left(x-\frac{4\sqrt{26537347}+26489}{11707}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 1375, ka 0.

$$factor(0x^{3}-11707x^{2}+52978x-23667)$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$factor(0-11707x^{2}+52978x-23667)$$

Tangohia te 23667 i te 0, ka -23667.

$$factor(-23667-11707x^{2}+52978x)$$

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.

$$-11707x^{2}+52978x-23667=0$$

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.

$$x=\frac{-52978±\sqrt{52978^{2}-4\left(-11707\right)\left(-23667\right)}}{2\left(-11707\right)}$$

Pūrua 52978.

$$x=\frac{-52978±\sqrt{2806668484-4\left(-11707\right)\left(-23667\right)}}{2\left(-11707\right)}$$

Whakareatia -4 ki te -11707.

$$x=\frac{-52978±\sqrt{2806668484+46828\left(-23667\right)}}{2\left(-11707\right)}$$

Whakareatia 46828 ki te -23667.

$$x=\frac{-52978±\sqrt{2806668484-1108278276}}{2\left(-11707\right)}$$

Tāpiri 2806668484 ki te -1108278276.

$$x=\frac{-52978±\sqrt{1698390208}}{2\left(-11707\right)}$$

Tuhia te pūtakerua o te 1698390208.

$$x=\frac{-52978±8\sqrt{26537347}}{2\left(-11707\right)}$$

Whakareatia 2 ki te -11707.

$$x=\frac{-52978±8\sqrt{26537347}}{-23414}$$

Nā, me whakaoti te whārite x=\frac{-52978±8\sqrt{26537347}}{-23414} ina he tāpiri te ±. Tāpiri -52978 ki te 8\sqrt{26537347}.

$$x=\frac{8\sqrt{26537347}-52978}{-23414}$$

Whakawehe -52978+8\sqrt{26537347} ki te -23414.

$$x=\frac{26489-4\sqrt{26537347}}{11707}$$

Nā, me whakaoti te whārite x=\frac{-52978±8\sqrt{26537347}}{-23414} ina he tango te ±. Tango 8\sqrt{26537347} mai i -52978.

$$x=\frac{-8\sqrt{26537347}-52978}{-23414}$$

Whakawehe -52978-8\sqrt{26537347} ki te -23414.

$$x=\frac{4\sqrt{26537347}+26489}{11707}$$

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 \frac{26489-4\sqrt{26537347}}{11707} mō te x_{1} me te \frac{26489+4\sqrt{26537347}}{11707} mō te x_{2}.

$$-11707x^{2}+52978x-23667=-11707\left(x-\frac{26489-4\sqrt{26537347}}{11707}\right)\left(x-\frac{4\sqrt{26537347}+26489}{11707}\right)$$