EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Problem2.6c:

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Answer: 2.804248(rounded)

Solution:

First make a note of the fact that you cannot take the square root of a negative number. Therefore, tex2html_wrap_inline85




Rewrite the radical terms as exponential terms

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Raise both sides of the equation to the power 8 and simplify.

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Solve using the quadratic formula.

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The answers are 2.804248 (rounded) and 0.445752 (rounded).




Check the solution by substituting 2.804248 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

Since the left side of the original equation after we substituted 2.804248 for x, then x = 2.804248 is a solution.




Since the solution x=0.445752 is not tex2html_wrap_inline95 (the domain), it cannot be a solution. However, if you forgot this fact, you can discover the same thing by checking the equation.




Check the solution by substituting 0.445752 in the original equation for x. If the left side of the equation equals the right side of the equation after the substitution, you have found the correct answer.

No solution because one of the terms is undefined over the set of real numbers.




You can also check the answer by graphing the equation:

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The graph represents the right side of the original equation minus the left side of the original equation. Since there is one x-intercept at 2.804248, the solution is 2.804248.
If you would like to review the solution for problem 2.6d, click on Solution.

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Author:Nancy Marcus

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