SOLVING A RADICAL EQUATION

SOLVING A RADICAL EQUATION WITH UNLIKE ROOT.

Hello everyone!
         In this class we are going to learn how to solve a radical equation. Radical equation are the same, and today we are going to solve one them.


   Normally, in solving a radical equation we are trying to take one of the radical term to other side and then isolate the other term. Typically we are going to take the cube root of both side, and that is going to be massive.

              So, here we are going to apply another method which is going be a substitution method. 
         Now we have this equation in a single variable, for the time being Iam going to turn it in to more variables.
          The first thing Iam going to do is that to replace the first radical with m and the second radical with n. So that the whole equation will change into 

m + n = 1

Now from there i can get more equations and name them as equation 1, 2, and 3.

Hence, we have three equations with three variables, but some variables are not linear, so let me try to write everything pretty much in terms of x. So from equation above i can isolate m and have equation 4 and isolate x from equation 3 and have equation 5.
   
     


Now i can go ahead and use equation 2 by substituting equation 4  and  5 in it.



Now let me simplify the parentheses:

Therefore the values of n are:


Now we equation 4 above is the relationship between x and n, so i can use it to find the all possible values of x



Finally we have the values of x .

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