Download 11.3 – Solving Radical Equations

11.3
Solving Radical Equations
11.3 – Solving Radical Equations
Goals / “I can…”
Solve equations containing radicals
Identify extraneous solutions
11.3 – Solving Radical Equations
Inverse Operations
How would you solve the following
equation?
2
x  9
Solve by taking the SQUARE ROOT. Why?
Square roots and Squaring are inverse
operations… they “undo” eachother!
11.3 – Solving Radical Equations
Inverse Operations
So… consider this: How could you solve for
x now?
x 4
Solve by doing the inverse operation:
SQUARING!
 x
2
  4
x  16
2
11.3 – Solving Radical Equations
A Refresher on Inverses (opposites):
 Opposite of Multiply is ____________
 Opposite of Add is ____________
 Opposite of Divide is ____________
 Opposite of Subtract is ____________
 Opposite of squaring is ____________
 Opposite of square rooting is ____________
11.3 – Solving Radical Equations
A radical equation is an equation with a
radical in it.
x  4  20
11.3 – Solving Radical Equations
Try
x  6  30
11.3 – Solving Radical Equations
Steps to Solving Radical Eq.’s
Isolate the radicand – get all
radicands on one side and all
constants on the other.
Square both sides of the equation
Solve for x
CHECK YOUR ANSWER!!!!
11.3 – Solving Radical Equations
If there are square roots on both sides,
square both sides to get rid of them.
3x  4  5 x  6
11.3 – Solving Radical Equations
#1 Solve

x2  4 x

x  2  4  x 
2
2
x  2  16  8 x  x
0  14  9 x  x
Standard Form
2
2
0  x  9 x  14
2
0  ( x  7)( x  2)
x  7, 2
11.3 – Solving Radical Equations
Check
x2  4 x
x7
x2
72  47
22  42
9  3
4 2
3  3
22
x7
x2
11.3 – Solving Radical Equations
#2 Solution
5x  5  5
2
 5x  5   5
2
2
2
5 x  5  25
2
5 x  20  0 Standard Form
2
5( x  4)  0
5( x  2)( x  2)  0
2
x  2
11.3 – Solving Radical Equations
5x  5  5
2
Check
x2
x  2
5(2) 2  5  5
5(2) 2  5  5
5(4)  5  5
5(4)  5  5
25  5
25  5
x2
x  2
11.3 – Solving Radical Equations
An extraneous solution is a solution
that does not make the original
problem true.
11.3 – Solving Radical Equations
Example:
x 12  x
11.3 – Solving Radical Equations
Sometimes an equation has no
solution.
You can only know this by putting the
solution into the original equation.
3x  8  2
11.3 – Solving Radical Equations
 Solve:
x=
x+6
11.3 – Solving Radical Equations
Solve
2x + 6 = 4