EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Problem 2.4a:

tex2html_wrap_inline84

Answer:x=5.



Solution First make a note of the fact that you cannot take the square root of a negative number. The term tex2html_wrap_inline88 is valid only if tex2html_wrap_inline90 and the term tex2html_wrap_inline92 is valid if tex2html_wrap_inline94 . The restricted domain must satisfy both of these constraints. Therefore, the domain is the set of real numbers tex2html_wrap_inline96 .





Since tex2html_wrap_inline92 is already isolated, we square both sides of the equation.

eqnarray22





Isolate the tex2html_wrap_inline100 term.

eqnarray31





Square both sides of the equation.

eqnarray34





Simplify the equation by dividing both sides by 81.

eqnarray42





Solve for x using the quadratic formula.

eqnarray45





There is one exact answer of 5.





Check the solution 5 by substituting 5 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=5.





You can also check the answer by graphing the equation:

displaymath82

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 5, we have verified the solution.


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

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Author:Nancy Marcus

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