Chapter 1.9, Problem 40E

To determine

To calculate: The value of $x$ from the equation $2x^5-243=0$ by algebraic method and graphical method.

Answer to Problem 40E

The value of $x$ is $2.611$ and the graph of the equation $2x^5-243=0$ provided below,

  

Explanation of Solution

Given information:

The equation $2x^5-243=0$ .

Calculation:

It is provided that the equation $2x^5-243=0$ .

Algebraic method;

The method in which isolate $x$ on one side of the equation and solve the value of $x$ .

From the equation $2x^5-243=0$ .

Add 265 on the both side of the equation,

  $\begin{array}{l}2x^5-243+243=243\\ 2x^5=243\end{array}$

Further solve for the value of $x$ ,

  $\begin{array}{l}{x}^5=\frac{243}{2}\\ x=\sqrt[\frac{1}{5}]{\frac{243}{2}}\\ x=2.611\end{array}$

Therefore, the value of $x=2.611$ .

Graphical method;

Let put $y_1=2x^5$ and $y_2=243$

The graph of the equation $y_1=2x^5$ provided below,

  

The graph of equation $y_2=243$ is provided below,

  

The graph of both equations in same figure is provided below,

  

The solution is the $x$ coordinate of the intersection point of the two graphs. The intersection point on the $x$ coordinate is $2.611$ .

Thus, the value of $x$ is $2.611$ .