Whakaoti i te x^3+3px^2+3qx+r=0

$$x ^ { 3 } + 3 p x ^ { 2 } + 3 q x + r = 0$$

Whakaoti mō p

$$\left\{\begin{matrix}p=-\frac{x^{3}+3qx+r}{3x^{2}}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&x=0\text{ and }r=0\end{matrix}\right.$$

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.

$$3px^{2}+3qx+r=-x^{3}$$

Tangohia te 3qx mai i ngā taha e rua.

$$3px^{2}+r=-x^{3}-3qx$$

Tangohia te r mai i ngā taha e rua.

$$3px^{2}=-x^{3}-3qx-r$$

He hanga arowhānui tō te whārite.

$$3x^{2}p=-x^{3}-3qx-r$$

Whakawehea ngā taha e rua ki te 3x^{2}.

$$\frac{3x^{2}p}{3x^{2}}=\frac{-x^{3}-3qx-r}{3x^{2}}$$

Mā te whakawehe ki te 3x^{2} ka wetekia te whakareanga ki te 3x^{2}.

$$p=\frac{-x^{3}-3qx-r}{3x^{2}}$$

Whakawehe -x^{3}-3qx-r ki te 3x^{2}.

$$p=-\frac{qx+\frac{r}{3}}{x^{2}}-\frac{x}{3}$$

Whakaoti mō q

$$\left\{\begin{matrix}q=-px-\frac{x^{2}}{3}-\frac{r}{3x}\text{, }&x\neq 0\\q\in \mathrm{R}\text{, }&x=0\text{ and }r=0\end{matrix}\right.$$

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.

$$3px^{2}+3qx+r=-x^{3}$$

Tangohia te 3px^{2} mai i ngā taha e rua.

$$3qx+r=-x^{3}-3px^{2}$$

Tangohia te r mai i ngā taha e rua.

$$3qx=-x^{3}-3px^{2}-r$$

He hanga arowhānui tō te whārite.

$$3xq=-x^{3}-3px^{2}-r$$

Whakawehea ngā taha e rua ki te 3x.

$$\frac{3xq}{3x}=\frac{-x^{3}-3px^{2}-r}{3x}$$

Mā te whakawehe ki te 3x ka wetekia te whakareanga ki te 3x.

$$q=\frac{-x^{3}-3px^{2}-r}{3x}$$

Whakawehe -x^{3}-3px^{2}-r ki te 3x.

$$q=-px-\frac{x^{2}}{3}-\frac{r}{3x}$$