essential question: describe the procedure for solving a radical equation
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Essential Question: Describe the procedure for solving a radical equation
A radical equation is an equation that has a variable in a radicand or a variable with a rational exponent. radical equation radical equation not a radical equation
To solve a radical equation, isolate the radical on one side of the equation and then raise both sides of the equation to the inverse power.
3 10x 23( 2) 25x
3 10x
Example: Goal is to get by
itself Subtract 2 from both
sides Inverse of square
root? Square each side Add 2 to both sides Divide both sides by 3
2 3 2 6x 3 2x 3 2 4x
2 2
3 2 4x 3 2 16x 3 18x 6x
YOUR TURN 5 1 6 0x 5 1 6x
2 2
5 1 6x 5 1 36x 5 35x 7x
Example: Goal is to get by itself Divide both sides by 2 Inverse of 2/3 power?
Take each side to 3/2 power
Use absolute values only when taking an even root
Make two equations
Add 2 to both sides
232 2 50x
23( 2)x
232 25x
3
32 23 22 25x
2 125x
2 125 2 125x or x 127 123x or x
Example:
322 3 54x
323 27x
2
3 232 33 27x
3 9x 6x
AssignmentPage 3941 – 12All problemsShow work
Essential Question: Describe the procedure for solving a radical equation
Much like with absolute value equations, you’ll have to check for extraneous solutions.
Part 1 – Solving the problem Get by itself Subtract 5, both sides Square both sides FOIL right side Subtract x & add 3 Factor Solve each
parenthesis
3 5x x 3 5x x
2 2
3 5x x 23 10 25x x x
20 11 28x x 0 ( 4)( 7)x x 4 7x or x
3x
Part 2 – Checking for extraneous solutions Original Problem Two solutions
The only solution is x = 7
3 5x x 4 7x or x x = 4 x = 7
Plug in for all x’s
Simplify under radical
Simplify radical
Combine like terms
Extraneous Real
4 3 5 4 7 3 5 7 1 5 4 4 5 7 1 5 4 2 5 7 6 4 7 7
YOUR TURN
5 1 3x x 5 1 3x x
2 2
5 1 3x x 25 1 6 9x x x
20 11 10x x 0 ( 10)( 1)x x 10 1x or x
Part 2 – Checking for extraneous solutions Original Problem Two solutions
x = 10 x = 1
5 10 131 0 5 11 3 1
10 1 05 3 5 1 3 1 49 3 10 4 3 1 7 13 0 2 13
5 1 3x x 10 1x or x
Real Solution
Extraneous Solution
The only solution is x = 10
Get the two equations on opposite sides
Raise both sides to eliminate the smallest power
FOIL the left sideGet equation = 0
Subtract 3x on both sides Subtract 4 on both sides
Factor the equation
Solve each parenthesis
0.5 0.252 1 3 4 0x x
0.5 0.252 1 3 4x x
4 40.5 0.252 1 3 4x x
22 1 3 4x x 24 4 1 3 4x x x 24 3 0x x
(4 3)( 1) 0x x (4 3) 0 ( 1) 0x or x
34 1x or x
Part 2 – Checking for extraneous solutions Original
Problem Two solutions
Let’s check x = -1
x = 3/4
Plug in for all x’s
Simplify parenthesis
Calculator is your friend
Combine like terms
Real Solution
0.5 0.252 1 3 4 0x x
34 1x or x
0.5 0.253 34 42 1 3 4 0
5 250.5 0
2 4
.250
25 52 2
0.250.50
0.55 52
5
2
0.0
Part 2 – Checking for extraneous solutions Original
Problem Two solutions
¾ is the only real solution
x =-1
Plug in for all x’s
Simplify parenthesis
Extraneous Solution
0.5 0.252 1 3 4 0x x
34 1x or x
0.5 0.252 1 3 4 01 1
0.5 0.251 1 0
(-1)0.5 is not a real number
YOUR TURN
3 2 2 7 0x x 3 2 2 7x x
2 2
3 2 2 7x x 3 2 2 7x x 2 7x 5x
AssignmentPage 394 - 39515 – 29Odd problemsShow work
Note: All problems have at least one real solution. Some will also have one extraneous solution & the book will not give you the extraneous solution, but I want both.