Warm-up
• Find the domain and range from these 3
equations.
y  3x  1  4
y  2 6 x  5  2
y  3 7 x  3  1
y  3x  1  4
1
D :[ , )
3
R :[4, )
y  2 6 x  5  2
5
D :[ , )
6
R : (, 2]
y  3 7 x  3  1
3
D : (, ]
7
R :[1, )
Chapter 6
Section 6-6
Radical Equations
Objectives
• I can solve equations containing radicals
• I can solve equations containing rational
exponents
• I can determine if a solution is Extraneous
Solving Radical Equations
•
•
•
•
Follow the same rules as any equation
Variable on left
Numbers on Right
Check your answers
Undoing The Square Root
•
•
•
•
We undo addition with subtraction
We undo multiplication with division
How do we undo the square root?
We square it!!
Undoing Radicals
2x  1
( 2 x  1)
2
( 3x  2 )
3
3x  2
( 6x  5)
4
6x  5
3
4
Radical Equations
• When solving radical equations make sure
only the radical is on the left when you
start the problem. (This is like solving
absolute value)
• ALWAYS Check answers. You may get
Extraneous Solutions from radicals.
Example 1
2x  8  5  1
2x  8  6
( 2x  8)  6
2
2x  8  36
2 x  28
x  14
2
Example 2
3  3 x 1  6
3
x 1  3
( 3 x  1) 3  3 3
x  1  27
x  28
Example 3
x  4  4 1
x  4  3
( x  4)  (3)
2
x49
x5
No Solution
2
Example 4
• .
2x  6  x  3
( 2x  6 )  ( x  3)
2
2x  6  x  3
x6  3
x9
2
Undoing Rational Exponents
• We undo the square root by Squaring It
• We undo a rational exponent by using the
Reciprocal of that exponent
Undoing Rational Exponents


2
x

1

 


2
3
4


5
3
x

4




3
2
5
4
2x  1
3x  4
EXAMPLE 4
Solve an equation with a rational exponent
Solve (x + 2)3/4 – 1 = 7.
(x + 2)3/4 – 1 = 7
(x + 2)3/4 = 8
(x +
2)3/4
4/3
= 84/3
Write original equation.
Add 1 to each side.
Raise each side to the power 4 .
3
x + 2 = (23)4/3
Apply properties of exponents.
x + 2 = 24
Simplify.
x + 2 = 16
Simplify.
x = 14
Subtract 2 from each side.
Homework
• Worksheet 10-5