College Algebra

Directions: Solve graphically:

x^(2/3)+x^(1/3)-2=0

I just don't know how to approach this?!

let x^(1/3) = t

so t^2 + t - 2 = 0
(t+2)(t-1) = 0
t = -2 or t=1

x^(1/3) = -2 or x^(1/3) = 1
x = -8 or x = 1

Don't know how solving this "graphically" can be easier?
Are you supposed to use a graphing calculator?

Thats just what the directions say..

But thank you so much, You Rock!!

To solve the equation graphically, you need to plot the graph of the equation and find the x-values where the function intersects the x-axis (i.e., where it is equal to zero). Here's how you can approach it step-by-step:

Step 1: Rearrange the equation
Re-write the equation in terms of a single root (x raised to an exponential power) by substituting a variable. Let's say, y = x^(1/3). Now you can express the equation as y^2 + y - 2 = 0.

Step 2: Graph the equation
Plot the graph of the equation y^2 + y - 2 = 0. To do this, you can consider different values of y between a suitable range (for example, -3 to 3) and find corresponding x-values using the substitution y = x^(1/3).

Step 3: Find the x-intercepts
Locate the points on the graph where the equation y^2 + y - 2 = 0 intersects the x-axis (i.e., where y = 0). These points correspond to the x-values that are solutions to the original equation x^(2/3) + x^(1/3) - 2 = 0.

Step 4: Determine the solutions
By finding the x-values where the graph intersects the x-axis, you can identify the solutions to the original equation x^(2/3) + x^(1/3) - 2 = 0.

Once you have the solutions, you can verify them by substituting them back into the original equation to ensure they satisfy the equation.

Alternatively, you can also solve the equation algebraically by performing a substitution and factoring to find the solutions.