Transcript 7.6 Solving Radical Equations

3.6 Solve Radical Equations
p.204
How do you solve a radical equation?
What must you do when you solve an
equation with two radicals?
What is an extraneous solution?
Ex: Solve for x.
x 3
Don’t forget to
check your
solutions!!
 x  3
2
2 **
x9
** Use this idea to solve the radical equations.
Write original equation.
Cube each side to eliminate the radical.
2x+7 = 27
2x = 20
x = 10
Simplify.
Subtract 7 from each side.
Divide each side by 2.
Check x = 10 in the original equation.
Substitute 10 for x.
Simplify.
Solution checks.
Ex: Solve for y.
5 4 y  0
 4 y  5
Don’t forget to
check your
solutions!!
4
y 5
 y  5
4
4
y  625
4
Ex: Solve.
(b) 2 x  8  4  6
4
3
(a) 3x  243
2 x  8  10
4
3
x  81

x


4
3
3
4

  81


x
 81
3
4
3
4
x   3
3
x  27
Don’t forget to
check your
solutions!!


2
2 x  8  10 2
2x  8  100
2x  92
x  46
Ex: Solve.
(a)
12  2 x  2 x  0
(b)
12  2 x  2 x
4 x  28  3 2 x
 12  2 x   2 x 
2
4 x  28  3 2 x  0
2
12  2x  4x

4 x  28
  3
2
2x
4x  28  9  2x
4x  28  18x
12  6x
2 x
28  14x
2 x
Don’t forget to
check your
solutions!!

2
Ex: Solve.
x  4  2x
x  4
2
  2x 
2
x  4x  4  2x
8  4  2 8
2  4  22
4  16
2  4
2 2
44
x 2  8 x  16  2 x
x 2  10 x  16  0
x  8x  2  0
x 8  0
x2  0
x 8
x2
Solution
Factor this to solve!
Don’t forget to
check your
solutions!!
Only use
the positive
answers
when
checking
solutions.
So, why didn’t one of the
solutions work?
• The solution that did not work is called
an extraneous solution.
• An extraneous solution is a false
solution.
• This is the reason why you MUST
check all solutions!!
• How do you solve a radical equation?
Isolate the radical on one side of the equation and
raise the equation to the power in the problem
to eliminate the radical.
• What must you do when you solve an equation
with two radicals?
Put a radical on each side of the equal sign before
raising to the power of the radical.
• What is an extraneous solution?
A answer that is not a valid solution of the
original problem.
3.6 Assignment
Page 208, 5-12, 1420, 56