Transcript RadicalEqns

6.5 SOLVING SQUARE ROOT
EQUATIONS
REAL-WORLD EXAMPLE
GOALS
Isolate the radical.
 Square both sides of an equation.
 Foil properly.

EXAMPLE 1.
3  2x  3  8
2x  3  5
2
2
2x  3  (5)
2x

3

25

2x  28
x  14


Isolate the radical.
Square both sides.
Add 3 to both sides.
Divide each side by 2.
x  7 5  x
EXAMPLE 2.
x 7  x 5
Isolate the radical.
 x  7   x  5

2
2
x  7  x 10x  25

Square both sides.
*(FOIL the right-hand side).
2
0  x  9x 18
2
Combine like terms.
0  x  3x  6
x  3 x  6
Factor.
Solve.
x  7 5  x
EXAMPLE 2 (NOT DONE YET!)
We have to check for extraneous solutions.
x  3
x  6

x  7 5  x
3  7  5  3

4  5  3
2  5 3
3 3
x  7 5  x
6  7  5  6
1  5  6
1  5  6

4  6 
3x 1  x 1  2
EXAMPLE 3.
Choose one of the radicals to isolate.
3x 1  x 1  2
3x 1  2  x 1



 
3x 1  2 
2

x 1
3x 1  2  x 1
STOP.
How do you FOIL something like
that???

2
2
Square both sides.
3x 1  x 1  2
EXAMPLE 3 (CONT.)
2 
x 1
  2 
2


x 1 2  x 1
4  2 x 1  2 x 1  x 1
F
O
I
 4  4 x 1  x 1
 x  5  4 x 1
Back to the problem…
L
3x 1  x 1  2
EXAMPLE 3 (CONT.)


3x 1  2  x 1

2
(Where we left off).
3x 1  x  5  4 x 1
Combine like terms while
isolating the radical.
2x  4  4 x 1
1
Divide both sides by 4.
x 1  x 1
2
2
2
1

Square both sides.
 x 1  x 1
2



EXAMPLE 3 (CONT.)
1 2
x  x 1  x 1
4
1 2 
x  2x  0
4
1
x x  8  0
4
x 0
x 8
3x 1  x 1  2
Combine like terms.
Factor.
Solve.

EXAMPLE 3 (CONT).
x 0
3x 1  x 1  2
is the only extraneous solution to this problem.
3x 1  x 1  2

3(0) 1  (0) 1  2
0 1  1  2
1 12
1 1  2
02

YOU TRY!
1.
3x  7  x 1
2.
5  x  x 1
3.
3 x  x 2  3
ANSWERS
1.
x 6
2.
x 1

3.


x  1
x 2
GROUPS OF 4 OR 5!
Your group will need…
• 1 radical equation worksheet PER PERSON
• 1 crumbled-up piece of paper
WE’LL BE PLAYING…
HOW TO PLAY…
Every person in your group gets a worksheet.
 As the music plays, your group will be passing
around the crumbled-up piece of paper.
 When the music stops, the person holding the
piece of paper must walk the group through a
problem (everyone does it together).
 The object is to not get stuck holding the paper!
 Go in sequential order (e.g. 1, 2, 3, 4, …).
