EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Problem 2.4b:

tex2html_wrap_inline76

Answer:x = 15.95 (rounded)

Solution:

First make a note of the fact that you cannot take the square root of a negative number. The term tex2html_wrap_inline80 is valid only if tex2html_wrap_inline82 and the term tex2html_wrap_inline84 is valid if tex2html_wrap_inline86 . The restricted domain must satisfy both of these constraints. Therefore, the domain is the set of real numbers tex2html_wrap_inline88





Since tex2html_wrap_inline84 is already isolated, we square both sides of the equation.

eqnarray18





Isolate the tex2html_wrap_inline92 term.

displaymath72





Square both sides of the equation.

eqnarray28





Solve for x using the quadratic formula.

eqnarray36





There are two approximate (rounded) answers: x = 15.95, 7.22





Check the solution 15.95 by substituting 15.95 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=15.95.





Check the solution 7.22 by substituting 7.22 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 x=7.22 is not valid.





You can also check the answer by graphing the equation:

displaymath73

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 15.95, we have verified that the only solution is 15.95.




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

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Author:Nancy Marcus

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