section 7.6 solving radical equations the power principle for equations if a = b then a n = b n ...
TRANSCRIPT
7.6 1
Section 7.6 Solving Radical Equations The Power Principle for Equations
If A = B then An = Bn
The Danger in Solving an Equivalent Equation Equations Containing One Radical Equations Containing Two Square Roots
7.6 2
Definitions A Radical Equation must have at least one radicand
containing a variable
The Power Rule: If we raise two equal expressions to the same power, the results
are also two equal expressions If A = B then An = Bn for any n Warning: These are NOT equivalent Equations!
When n is even, you MUST check answers in the original equation
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7.6 3
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 x2 = 9 has two solutions x = 3 and x = -3 Checking solutions in the original x = 3:
3 = 3 is true, so x = 3 is OK -3 = 3 is untrue, so discard x = -3
7.6 4
Equations Containing One Radical To eliminate the radical,
raise both sides to the index of the radical
13
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:
Check
7.6 5
Sometimes, You Need toIsolate the Radical Get the radical alone before raising to a power
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discard
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7.6 6
More Examples 1
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7.6 7
More Examples 2
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7.6 8
More Examples 3
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7.6 9
More Examples 4
63
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7.6 10
Equations Containing Two Radicals Make sure radicals are on opposite sides Sometimes you need to repeat the process
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7.6 11
What Next? Complex Numbers! Present Section 7.8
7.7 Is Not Covered