Download 6.6 NOTES: Solving Radical Equations and Inequalities

6.6
RADICAL EQUATIONS
FOR THIS SECTION WE WILL ASSUME THAT ALL VARIABLES ARE POSITIVE!!!
Steps 1 and 2 are interchangeable as to which is done first.
1. Isolate the term containing the radical if possible.
2. Use index to determine power needed for each side in order to eliminate the radical sign.
3. Solve for the variable.
4. Check for extraneous solutions. (solutions that do not satisfy the original equation)
Solve over the set of real numbers.
3
1.
x 1  4
3.
5.
3x  4  2 x  10
3  x  12
6.6 extension
2. x – 4 = x 3
4.
6. x
x  x 5 1
2
3
 12
SOLVING RADICAL INEQUALITIES
FOR THIS SECTION WE WILL ASSUME THAT ALL VARIABLES ARE POSITIVE!!!
1. Setup 2 cases. Case 1 is to solve the radicand for > 0 to identify excluded values and Case 2 is to solve
the original inequality for the variable.
2. Create a number line and place critical points from step 1 on the number line.
3. Test critical points AND values on the number line in between critical points to see which sections
work.
Solve over the set of real numbers.
 4  3x  2
3  4 x  5  10
1.
2.