EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Example 5:

tex2html_wrap_inline221

First make a note of the fact that you cannot take the square root of a negative number. Therefore,the term tex2html_wrap_inline223 is valid only if tex2html_wrap_inline225 and the term tex2html_wrap_inline227 is valid if tex2html_wrap_inline229 . The restricted domain must satisfy both of these constraints. Therefore, the domain is the set of real numbers tex2html_wrap_inline231





Isolate the term tex2html_wrap_inline227 by adding 3 to both sides of the equation.

eqnarray29





Square both sides of the equation.

eqnarray35





Isolate the tex2html_wrap_inline235 term.

eqnarray51





Square both sides of the equation.

eqnarray85





Solve for x using the quadratic formula.

eqnarray108





There are two approximate answers, 8163.162 and 18.8385.





Check the solution 8163.162 by substituting 8163.162 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=8163.162.





Check the solution 18.8385 by substituting 18.8385 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 does not equal the right side of the original equation after we substituted our solution for x, the solution 18.8385 is not a valid solution.





You can also check the answer by graphing the equation:

displaymath219

.

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 x-intercept is 8163.162, we have verified the solution.


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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