11.3 Solving Radical Equations. 11.3 – Solving Radical Equations Goals / “I can…” Solve...
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Transcript of 11.3 Solving Radical Equations. 11.3 – Solving Radical Equations Goals / “I can…” Solve...
11.3
Solving Radical Equations
11.3 – Solving Radical Equations
Goals / “I can…”Solve equations containing radicalsIdentify extraneous solutions
Inverse OperationsHow would you solve the following
equation?
Solve by taking the SQUARE ROOT. Why?
Square roots and Squaring are inverse operations… they “undo” eachother!
2 9x
11.3 – Solving Radical Equations
Inverse OperationsSo… consider this: How could you solve
for x now?
Solve by doing the inverse operation: SQUARING!
4x
2 2
4x
16x
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
11.3 – Solving Radical Equations
A radical equation is an equation with a radical in it.
204 x
11.3 – Solving Radical Equations
Try
306 x
Steps to Solving Radical Eq.’sSteps to Solving Radical Eq.’sIsolate the radicand – get all
radicands on one side and all constants on the other.
Square both sides of the equationSolve for xCHECK YOUR ANSWER!!!!
11.3 – Solving Radical Equations
11.3 – Solving Radical Equations
If there are square roots on both sides, square both sides to get rid of them.
6543 xx
#1 Solve xx 42
2242 xx
28162 xxx 29140 xx
1490 2 xx
)2)(7(0 xx
2 ,7x
Standard Form
11.3 – Solving Radical Equations
Check
7x 2x
7427
39
33
7x
xx 42
2422
24
22
2x
11.3 – Solving Radical Equations
#2 Solution
22
2 555 x
2555 2 x
0205 2 x
2x
555 2 x
0)4(5 2 x
0)2)(2(5 xx
Standard Form
11.3 – Solving Radical Equations
Check2x 2x
555 2 x
55)2(5 2
55)4(5
525
2x
55)2(5 2
55)4(5
525
2x
11.3 – Solving Radical Equations
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:
xx 12
11.3 – Solving Radical Equations
Sometimes an equation has no solution.
You can only know this by putting the solution into the original equation.
283 x
11.3 – Solving Radical Equations
Solve:
x = x + 6
11.3 – Solving Radical Equations
Solve
2x + 6 = 4