EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Example 1:

tex2html_wrap_inline53

First make a note of the fact that you cannot take the square root of a negative number. Therefore,the tex2html_wrap_inline55 term is valid only if tex2html_wrap_inline57 and the second term tex2html_wrap_inline59 is valid if tex2html_wrap_inline61




Isolate the tex2html_wrap_inline63 term.

displaymath51




Square both sides of the equation.

eqnarray19




Isolate the tex2html_wrap_inline65 term.

eqnarray27




Square both sides of the equation.

eqnarray30




Check the solution by substituting 9 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, then there is no solution.




You can also check the answer by graphing the equation:

eqnarray34

.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 are no x-intercepts, there are no solutions.


If you would like to review another example, click on Example

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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