EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Example 4:

tex2html_wrap_inline98

First make a note of the fact that you cannot take the square root of a negative number. Therefore,the term tex2html_wrap_inline100 is valid only if tex2html_wrap_inline102 and the term tex2html_wrap_inline104 is valid if tex2html_wrap_inline106 . The restricted domain must satisfy both of these constraints. Therefore, the domain is the set of real numbers tex2html_wrap_inline108





Since tex2html_wrap_inline104 is already isolated, we square both sides of the equation.

eqnarray22





Isolate the tex2html_wrap_inline112 term.

displaymath92





Square both sides of the equation.

eqnarray32





Simplify the equation by dividing both sides by 3.

displaymath93





Solve for x using the quadratic formula.

eqnarray42





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





Check the solution -8 by substituting -8 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=-8.





Check the solution -37.333 by substituting -37.333 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, the solution -37.333 is not a valid solution.





You can also check the answer by graphing the equation:

displaymath94

.

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-intercept is -8, we have verified the solution.


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.

If you would like to go back to the equation table of contents, click on Contents.

[Algebra] [Trigonometry]
[Geometry] [Differential Equations]
[Calculus] [Complex Variables] [Matrix Algebra]

S.O.S MATHematics home page

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Author:Nancy Marcus

Copyright 1999-2017 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour