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Published byPatricia Wheeler Modified over 9 years ago
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Solving Radical Inequalities
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Solving radical inequalities is similar to solving rational equations, but there is one extra step since we must make sure the radical is a real number, i.e. the radicand must be greater than or equal to zero.
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Example 1 Solve Since the radical must be a real number, must be greater than or equal to zero.
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Square both sides Subtract 2 from both sides We know that both and must be true.
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Check a value of in the original inequality. The solution is all real numbers such that. [Note: this takes care of also]
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Example 2 Solve Since each radical must be a real number, for the first radical so and for the other radical. makes both radicals real.
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Solve Isolate one radical Square both sides Simplify (continued on next slide)
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(continued from previous slide) Isolate one variable Square both sides Simplify and solve Noting also that, the solution is, approximately.
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Check your answer by substituting a value for x in the original inequality.
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