Whakaoti i te x^3-px-q=0

$$x ^ { 3 } - p x - q = 0$$

Whakaoti mō p (complex solution)

$$\left\{\begin{matrix}p=\frac{x^{3}-q}{x}\text{, }&x\neq 0\\p\in \mathrm{C}\text{, }&q=0\text{ and }x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te x^{3} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-px-q=-x^{3}$$

Me tāpiri te q ki ngā taha e rua.

$$-px=-x^{3}+q$$

He hanga arowhānui tō te whārite.

$$\left(-x\right)p=q-x^{3}$$

Whakawehea ngā taha e rua ki te -x.

$$\frac{\left(-x\right)p}{-x}=\frac{q-x^{3}}{-x}$$

Mā te whakawehe ki te -x ka wetekia te whakareanga ki te -x.

$$p=\frac{q-x^{3}}{-x}$$

Whakawehe q-x^{3} ki te -x.

$$p=x^{2}-\frac{q}{x}$$

Whakaoti mō p

$$\left\{\begin{matrix}p=\frac{x^{3}-q}{x}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&x=0\text{ and }q=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te x^{3} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-px-q=-x^{3}$$

Me tāpiri te q ki ngā taha e rua.

$$-px=-x^{3}+q$$

He hanga arowhānui tō te whārite.

$$\left(-x\right)p=q-x^{3}$$

Whakawehea ngā taha e rua ki te -x.

$$\frac{\left(-x\right)p}{-x}=\frac{q-x^{3}}{-x}$$

Mā te whakawehe ki te -x ka wetekia te whakareanga ki te -x.

$$p=\frac{q-x^{3}}{-x}$$

Whakawehe -x^{3}+q ki te -x.

$$p=x^{2}-\frac{q}{x}$$

Whakaoti mō q

$$q=x\left(x^{2}-p\right)$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te x^{3} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-px-q=-x^{3}$$

Me tāpiri te px ki ngā taha e rua.

$$-q=-x^{3}+px$$

He hanga arowhānui tō te whārite.

$$-q=px-x^{3}$$

Whakawehea ngā taha e rua ki te -1.

$$\frac{-q}{-1}=\frac{x\left(p-x^{2}\right)}{-1}$$

Mā te whakawehe ki te -1 ka wetekia te whakareanga ki te -1.

$$q=\frac{x\left(p-x^{2}\right)}{-1}$$

Whakawehe x\left(-x^{2}+p\right) ki te -1.

$$q=x^{3}-px$$