EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Problem 2.3c:

tex2html_wrap_inline98

Answer: 0

Solution:

First make a note of the fact that you cannot take the square root of a negative number. Therefore, tex2html_wrap_inline100 .



Add 9x to both sides of the equation so that the radical term is

isolated.

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Square both sides of the equation:

tex2html_wrap_inline104

tex2html_wrap_inline106




Subtract 3x from and add 9 to both sides of the equation.

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Solve using factoring:

and or

tex2html_wrap_inline116



Check the solution x=0 by substituting 0 for x in the original equation. If after the substitution, the left side of the original equation equals the right side of the original equation, 0 is a solution.




Check the solution tex2html_wrap_inline128 by substituting -0.888889 for x in the original equation. If after the substitution, the left side of the original equation equals the right side of the original equation, -0.888889 is a solution.

Since the left side of the original equation does not equal the right side of the original equation after -0.888889 was substituted for x, then x=-0.888889 is not a solution.



You can also check the answer by graphing the equation:

displaymath74

The graph represents the right side of the original equation minus the left side of the original equation. There is one x-intercept, at the origin where x=0, therefore 0 is a solution to the equation.


If you would like to review the answer and solution to problem 2.3e, click on Solution.

If you would like to go back to the problem page, click on Problem.

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Author: Nancy Marcus

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