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Published bySuzanna Logan Modified over 5 years ago

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Section 7.6 Solving Radical Equations The Power Principle for Equations If A = B then A n = B n The Danger in Solving an Equivalent Equation Equations Containing One Radical Equations Containing Two Square Roots 7.61

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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 expressions to the same power, the results are also two equal expressions If A = B then A n = B n for any n Warning: These are NOT equivalent Equations! When n is even, you MUST check answers in the original equation 7.62

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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: x 2 = 3 2 which simplifies to x 2 = 9 x 2 = 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 7.63

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Equations Containing One Radical To eliminate the radical, raise both sides to the index of the radical 7.64

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Sometimes, You Need to Isolate the Radical Get the radical alone before raising to a power 7.65

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More Examples 1 7.66

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More Examples 2 7.67

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More Examples 3 7.68

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More Examples 4 7.69

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Equations Containing Two Radicals Make sure radicals are on opposite sides Sometimes you need to repeat the process 7.610

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What Next? Complex Numbers! Present Section 7.8 Present Section 7.8 7.7 Is Not Covered 7.611

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