Question

Use the graphical method to solve the equation in the indicated exercise form the Section 1.5. (Lesson 1.11)

$x^{\frac{1}{2}}+x^{\frac{1}{3}}-x=0;$$\left[-1,5\right]$

Short answer

The solution by graphically method is $x=0,3.32$.

Step-by-step solution

Step 1. Definition of the x-intercept.

x-intercept is the point where the value of y is 0.

Step 2. Draw the graph of the equation.

$x^{\frac{1}{2}}+x^{\frac{1}{3}}-x=0$;$\left[-1,5\right]$

Now, equate the left side of the equation to$y$Then sketch the graph of the equation on a graphing facility

Draw the graph:

Step 3. Solve the equation graphically.

The solutions to the given equations are the x-intercepts or the zeros of the graph.

So, identify the values of x-intercepts by using the trace function of the graphing utility.

Hence, the solutions or the zeros are$x=0$ and $3.32$.