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Radical
or irrational equations |
Solving
irrational or radical equations |
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Radical
or
irrational
equations |
Any
equation where the variable is inside a radical is called an
irrational equation. |
To solve
an irrational equation we should isolate one of the radicals on
one side of the equation and
get other radicals and terms on the other side of the
equation. |
Rise both sides of the equation to
a power to remove the radical, and then simplify and solve as we do with any equations.
Repeat the procedure until all radicals are removed. |
Substitute answers back into original equation to make sure that solutions are valid,
as there could be some additional or extraneous solutions that do not satisfy the original equation.
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That
is, raising equation
to a power can lead to extraneous
solutions. We must check to be
certain which of obtained values are true solutions. |
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Solving irrational
or radical
equations |
Example:
Solve the
irrational equation |
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Solution:
First isolate the radical and then square both sides
of the equation, |
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Checking
for the solutions: |
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Example:
Solve the
irrational equation |
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Checking
for the solutions: |
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College
algebra contents D |
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