EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Problem 2.4c:

tex2html_wrap_inline53
Answer:x = 36

Solution:

First make a note of the fact that you cannot take the square root of a negative number. The term tex2html_wrap_inline57 is valid only if tex2html_wrap_inline59 and the term tex2html_wrap_inline61 is valid if tex2html_wrap_inline63 . The restricted domain must satisfy both of these constraints. Therefore, the domain is the set of real numbers tex2html_wrap_inline65





Isolate the tex2html_wrap_inline61 is already isolated, we square both sides of the equation.

eqnarray18





Isolate the tex2html_wrap_inline57 term .

eqnarray26





Square both sides of the equation.

eqnarray30




The answer is 36.





Check the solution 36 by substituting 36 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 our solution for x, we have verified that the solutions is x = 36.





You can also check the answer by graphing the equation:

displaymath51

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 the only x-intercept is 36, we have verified that the only solution is 36.


If you would like to review the solution for problem 2.4d, click on Solution.

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Author:Nancy Marcus

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