solving radical equations
DESCRIPTION
Solving Radical Equations. The Power Rule Equations Containing One Radical Equations Containing Two Radicals. Definitions. A Radical Equation must have at least one radicand containing a variable The Power Rule : - PowerPoint PPT PresentationTRANSCRIPT
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Solving Radical Equations
The Power Rule Equations Containing One Radical Equations Containing Two Radicals
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Definitions A Radical Equation must have at least one
radicand containing a variable
The Power Rule: If we raise two equal quantities to the same power, the
results are also two equal quantities If x = y then xn = yn
Warning: These are NOT equivalent Equations!
2243 xxx
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Why are they not Equivalent? Start with a simple original equation: x = 3 Square both sides to get a new equation: x2 = 32 which simplifies to x2 = 9 The only solution to x = 3 is 3 x2 = 9 has two solutions 3 and -3 Raising both sides of the equation to an equal
power is called an irreversible step. Therefore we need to check our solutions to
make sure they are valid.
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Equations Containing One Radical To eliminate the radical,
raise both sides to the index of the radical
13
163
43
43
22
x
x
x
x
44
416
4313
:
Check
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Sometimes, You First Need to Isolate the Radical Get the radical alone before raising to a power
50:
0)5(
05
1213
113
113
113
2
2
22
andSolutions
xx
xx
xxx
xx
xx
xx
solutiongood
xCheck
discard
xCheck
514
5116
51115
511)5(3
5
02
0110
011)0(3
0
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Practice – on the board