EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS


Example 2:

tex2html_wrap_inline150

First make a note of the fact that you cannot take the square root of a negative number. Therefore, the tex2html_wrap_inline152 term is valid only if tex2html_wrap_inline154 the second term tex2html_wrap_inline156 is valid if tex2html_wrap_inline158 , and the term tex2html_wrap_inline160 is valid only if tex2html_wrap_inline162 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_inline164




Multiply both sides of the equation by 3 to remove the fraction.

eqnarray30




Square both sides of the equation and simplify.

eqnarray40




Isolate the tex2html_wrap_inline166 term and simplify.

eqnarray64





Square both sides of the equation and simplify.

eqnarray70




Use the quadratic formula to solve for x.

eqnarray83




The answers are tex2html_wrap_inline168




Check the solution 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 5 for x, then x=5 is a solution.




Check the solution by substituting 0.155505 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 0.155505 for x, then the solution x=0.155505 is a not valid and not a solution after all.





You can also check the answer by graphing the equation:

eqnarray117

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 5, then the only solution is x=5.


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Author:Nancy Marcus

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