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# Solving Equations with Radicals and Exponents

In the next example the even-root property is used to solve some equations that are a bit complicated.

Example 1

Using the even-root property

Solve each equation.

a) (x - 3)2 = 4

b) 2(x - 5)2 - 7 = 0

c) x4 - 1 = 80

Solution

 a) (x - 3)2 = 4 x - 3 = 4 or x - 3 = -2 Even-root 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 Even-root property x or x  x or x The solution set is c) x4 - 1 = 80 x4 = 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 even-root property as in parts (a) and (b) of Example 1. In the future you will learn general methods for solving any quadratic equation.