Solving Equations with Radicals and Exponents
In the next example the evenroot property is used to solve some equations that
are a bit complicated.
Example 1
Using the evenroot property
Solve each equation.
a) (x  3)^{2} = 4
b) 2(x  5)^{2}  7 = 0
c) x^{4}  1 = 80
Solution
a) (x  3)^{2} = 4 




x  3 = 4 
or 
x  3 
= 2 
Evenroot property 
x = 5 
or 
x 
= 1 
Add 3 to each side. 
The solution set is {1, 5}.
b) 2(x  5)^{2 } 7 
= 0 




2(x  5)^{2} 
= 7 



Add 7 to each side. 
(x  5)^{2} 




Divide each side by 2. 
x  5 

or 
x  5 

Evenroot property 
x 

or 
x 


x 

or 
x 


The solution set is
c) x^{4}  1 
= 80 
x^{4} 
= 81 
x 
= Â±
=
Â± 3 
The solution set is {3, 3}.
You probably know hou to solve quadratic equations by factoring. The quadratic
equations that we encounter in this chapter can be solved by using the evenroot property as in parts (a) and (b) of Example
1. In the future you will learn general
methods for solving any quadratic equation.
