Solving Radical Equations - Extraneous Roots

Category: Algebra

"Published in Newark, California, USA

Find the roots of the equation
 

Solution:

Consider the given equation
 

Square both sides of the equation
 

 

 

 

Square both sides of the equation again
 

 

 

 

Equate each factor to zero to solve for the value of x

For: x - 9 = 0                                                      For: x - 2 = 0
       x = 9                                                                  x = 2

Now, check the values of x to the given equation

If x = 9
 

 

 

 

                                         x = 9 is an extraneous root.

If x = 2
 

 

 

 

 

                                          x = 2 is a root.

Therefore, 2 is the root.