Download ( 2x 2 Solve a Radical Equation ( x 2 3 Check for Extraneous Solutions

EXAMPLE
2
Solve a Radical Equation
3 4 5, you need to isolate the radical
To solve the equation 2x
expression first.
2x
345
Write the original equation.
2x
31
Subtract 4 from each side of the equation.
(2x
3 )2 12
Square each side of the equation.
2x 3 1
Simplify the equation.
2x 4
Add 3 to each side of the equation.
x2
Divide each side of the equation by 2.
ANSWER 䊳
The solution is 2. Check the solution in the original equation.
Solve a Radical Equation
Solve the equation.
1. x
3
2. m
4 0
3. x
64
4. n
11
5. x
4 5 11
6. 3n
131
Squaring both sides of an equation can introduce a
solution to the squared equation that does not satisfy the original equation. Such a
solution is called an extraneous solution. When you solve by squaring both sides
of an equation, check each solution in the original equation.
EXTRANEOUS SOLUTIONS
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MORE EXAMPLES
3
Check for Extraneous Solutions
Solve x2 x and check for extraneous solutions.
NE
ER T
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INT
EXAMPLE
Solution
x2 x
Write the original equation.
(x2)2 x 2
Square each side of the equation.
x 2 x2
Simplify the equation.
x2 x 2 0
Write the equation in standard form.
(x 2)(x 1) 0
Factor the equation.
Use the zero-product property to solve for x.
CHECK
✓ Substitute 2 and 1 in the original equation.
2
2 ⱨ 2
22✓
ANSWER 䊳
x 2 or x 1
1
2 ⱨ 1
1 1
The only solution is 2, because x 1 does not satisfy the
original equation.
12.3
Solving Radical Equations
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