EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Example 4:

tex2html_wrap_inline224

First make a note of the fact that you cannot take the square root of a negative number. Therefore, the tex2html_wrap_inline226 term is valid only if tex2html_wrap_inline228 the term tex2html_wrap_inline230 is valid if tex2html_wrap_inline232 , and the term tex2html_wrap_inline234 is valid only if tex2html_wrap_inline236 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_inline238





Square both sides of the equation and simplify.

eqnarray41





Isolate the tex2html_wrap_inline240 term.

eqnarray95





Square both sides of the equation and simplify.

eqnarray102




Use the quadratic formula to solve for x.

eqnarray115




The answers are 15 and-0.078534.




Check the solution by substituting 15 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 15 for x, then x=15 is a solution.




Check the solution by substituting -0.078534 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 -0.078534 for x, then x=-0.078534 is not a real solution.




You can also check the answer by graphing the equation:

eqnarray150

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 15, then the only solution is x=15.


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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