EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Example 3:

tex2html_wrap_inline88

First make a note of the fact that you cannot take the square root of a negative number. Therefore, the tex2html_wrap_inline90 term is valid only if tex2html_wrap_inline92 the second term tex2html_wrap_inline94 is valid if tex2html_wrap_inline96 , and the term tex2html_wrap_inline98 is valid only if tex2html_wrap_inline100 The equation is valid if all three terms are valid, therefore the domain is restricted to the common domain of the three terms or the set of real numbers tex2html_wrap_inline102.




Square both sides of the equation and simplify.

eqnarray29





Isolate the tex2html_wrap_inline104 term and simplify.

eqnarray50





Square both sides of the equation and simplify.

eqnarray58



The answer is 3.




Check the solution by substituting 3 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 equals the right side of the original equation after we substituted 3 for x, then x=3 is a solution.





You can also check the answer by graphing the equation:

eqnarray76

The graph represents the right side of the original equation minus the left side of the original equation. The x-intercept(s) of this graph is(are) the solution(s). Since there is just one x-intercept at 3, then the only solution is x=3.


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If you would like to test yourself by working some problems similar to this example, click on Problem

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Author:Nancy Marcus

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