Whakaoti i te A*x^5-x=x

$$A \cdot x ^ { 5 } - x = x$$

Whakaoti mō A (complex solution)

$$\left\{\begin{matrix}A=\frac{2}{x^{4}}\text{, }&x\neq 0\\A\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me tāpiri te x ki ngā taha e rua.

$$Ax^{5}=x+x$$

Pahekotia te x me x, ka 2x.

$$Ax^{5}=2x$$

He hanga arowhānui tō te whārite.

$$x^{5}A=2x$$

Whakawehea ngā taha e rua ki te x^{5}.

$$\frac{x^{5}A}{x^{5}}=\frac{2x}{x^{5}}$$

Mā te whakawehe ki te x^{5} ka wetekia te whakareanga ki te x^{5}.

$$A=\frac{2x}{x^{5}}$$

Whakawehe 2x ki te x^{5}.

$$A=\frac{2}{x^{4}}$$

Whakaoti mō A

$$\left\{\begin{matrix}A=\frac{2}{x^{4}}\text{, }&x\neq 0\\A\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me tāpiri te x ki ngā taha e rua.

$$Ax^{5}=x+x$$

Pahekotia te x me x, ka 2x.

$$Ax^{5}=2x$$

He hanga arowhānui tō te whārite.

$$x^{5}A=2x$$

Whakawehea ngā taha e rua ki te x^{5}.

$$\frac{x^{5}A}{x^{5}}=\frac{2x}{x^{5}}$$

Mā te whakawehe ki te x^{5} ka wetekia te whakareanga ki te x^{5}.

$$A=\frac{2x}{x^{5}}$$

Whakawehe 2x ki te x^{5}.

$$A=\frac{2}{x^{4}}$$

Whakaoti mō x (complex solution)

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\sqrt[4]{2}iA^{-\frac{1}{4}}\text{; }x=\sqrt[4]{2}A^{-\frac{1}{4}}\text{; }x=-\sqrt[4]{2}A^{-\frac{1}{4}}\text{; }x=-\sqrt[4]{2}iA^{-\frac{1}{4}}\text{, }&A\neq 0\end{matrix}\right.$$

Whakaoti mō x

$$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=\sqrt[4]{\frac{2}{A}}\text{; }x=-\sqrt[4]{\frac{2}{A}}\text{, }&A>0\end{matrix}\right.$$