3-4 Radical Equations (Presentation)
-
Upload
sandra-miller -
Category
Documents
-
view
219 -
download
0
Transcript of 3-4 Radical Equations (Presentation)
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 1/14
3-4 Radical Equations
Unit 3 Quadratic and Polynomial Functions
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 2/14
Concepts and Objectives
Objective #13
Solve equations with radicals and check the solutions Solve equations that are quadratic in form
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 3/14
Power Property
If P and Q are algebraic expressions, then every
solution of the equation P = Q is also a solution of the equation P n = Qn, for any positive integer n.
Note: This does not mean that every solution of P n = Qn
is a solution of P = Q.
We use the power property to transform an equation
that is difficult to solve into one that can be solved more
easily. Whenever we change an equation, however, it is
essential to check all possible solutions in the original
equation.
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 4/14
Solving Radical Equations
Step 1 Isolate the radical on one side of the equation.
Step 2 Raise each side of the equation to a power that isthe same as the index of the radical to eliminate the
radical.
,
and 2.
Step 3 Solve the resulting equation.
Step 4 Check each proposed solution in the original
equation.
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 5/14
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 6/14
Solving Radical Equations
Example: Solve
Check:
− + =4 12 0 x x
= +4 12 x x
= +2
4 12 x x
− − =2
4 12 0 x x
( )− + =6 4 6 12 0
− =6 36 0
− =6 6 0
Solution: {6}
( )( )− + =6 2 0 x x
= −6, 2
=0 0
( )− − − + =2 4 2 12 0
− − =2 4 0
− − =2 2 0− ≠4 0
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 7/14
Solving Radical Equations
Example: Solve + − + =3 1 4 1 x
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 8/14
Solving Radical Equations
Example: Solve
Check:
+ − + =3 1 4 1 x
+ = + +3 1 4 1 x x
+ = + + + +3 1 4 2 4 1 x x x
− = +2 4 2 4 x x
( ) + − + =3 0 1 0 4 1
− =1 4 1
− =1 2 1
Solution: {5}
− = +2 4 x x
− + = +2
4 4 4 x x x
− =2
5 0 x x
( )− =5 0 x x
= 0, 5 x
− ≠
1 1( ) + − + =3 5 1 5 4 1
− =16 9 1
− =4 3 1=1 1
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 9/14
Quadratic in Form
An equation is said to be quadratic in form if it can be
written as
where a ≠ 0 and u is some algebraic expression.
+ + =2
0au bu c
To solve this type of equation, substitute u for the
algebraic expression, solve the quadratic expression for
u, and then set it equal to the algebraic expression and
solve for x . Because we are transforming the equation,you will still need to check any proposed solutions.
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 10/14
Quadratic in Form
Example: Solve ( ) ( )− + − − =2 3 1 3
1 1 12 0 x x
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 11/14
Quadratic in Form
Example: Solve
Let . This makes our equation:
( ) ( )− + − − =2 3 1 3
1 1 12 0 x x
( )= −
1 3
1u x
+ − =2
12 0u u
( )( )+ − =4 3 0u u
So, and= −4, 3u
( )− = −1 3
1 4 x ( )− =1 3
1 3 x
− = −1 64 x
= −63
− =1 27 x
= 28 x
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 12/14
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 13/14
Quadratic in Form
Example: Solve (cont.)( ) ( )− + − − =2 3 1 3
1 1 12 0 x x
( ) ( )− + − − =2 3 1 3
28 1 28 1 12 0
− =2 3 1 3
Solution: {–63, 28}
( ) ( )+ − =2 1
3 3 12 0
+ − =9 3 12 0
=0 0
8/8/2019 3-4 Radical Equations (Presentation)
http://slidepdf.com/reader/full/3-4-radical-equations-presentation 14/14
Homework
College Algebra
Page 144: 35-85 (×5s) Turn In: 50, 55, 60, 80