EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Example 3:

tex2html_wrap_inline96

First make a note of the fact that you cannot take the square root of a negative number. Therefore,the first term is valid only if tex2html_wrap_inline98 and the second term is valid if tex2html_wrap_inline100 . Therefore, the domain is restricted to the set of real numbers x, tex2html_wrap_inline102 .





Isolate the tex2html_wrap_inline104 term

displaymath92





Square both sides of the equation.

eqnarray23





Isolate the tex2html_wrap_inline106 term.

displaymath93





Square both sides of the equation.

eqnarray34





Solve for x using the quadratic formula.

eqnarray43





There is one exact answer of 4 and one approximate answer of -1.387755.





Check the solution 4 by substituting 4 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=4.





Check the solution -1.387755 by substituting -1.387755 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=-1.387755.





You can also check the answer by graphing the equation:

tex2html_wrap_inline130
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 4 and -1.387755, we have verified the solutions.


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