EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Example 2:
tex2html_wrap_inline84

First make a note of the fact that you cannot take the square root of a negative number. Therefore,the term tex2html_wrap_inline86 is valid only if tex2html_wrap_inline88 and the term tex2html_wrap_inline90 is valid if tex2html_wrap_inline92 We can meet both restrictions by requiring tex2html_wrap_inline94 .





Isolate the tex2html_wrap_inline86 term.

eqnarray18





Square both sides of the equation.

eqnarray22

eqnarray28





Isolate the tex2html_wrap_inline98 term.

eqnarray33





Square both sides of the equation and simplify.

eqnarray36





Set the equation equal to zero.

eqnarray43





Solve using the quadratic formula.

eqnarray46





Check the solution by substituting 190 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=190.





Check the solution by substituting 30 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=30.





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-intercepts are 30 and 190, we have verified the solution.


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Author:Nancy Marcus

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