EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Problem 2.3b:

tex2html_wrap_inline94

Answer: tex2html_wrap_inline96 (rounded)

Solution:

First make a note of the fact that you cannot take the square root of a negative number. Therefore, tex2html_wrap_inline98 .



Subtract 9x from both sides of the equation so that the radical term is

isolated.

displaymath66




Square both sides of the equation:

tex2html_wrap_inline102

tex2html_wrap_inline104




Subtract 3x and 2 from both sides of the equation.

displaymath67




Solve using the quadratic formula.

displaymath68




Simplify.

tex2html_wrap_inline108

tex2html_wrap_inline110

tex2html_wrap_inline96



Check the solution tex2html_wrap_inline110 by substituting 1.386897 for x in the original equation. If after the substitution, the left side of the original equation equals the right side of the original equation, 1.386897 is a solution.

Since the left side of the original equation does not equal the right side of the original equation after 1.386897 was substituted for x, then x=1.386897 is not a solution.

Check the solution x= 0.872362 by substituting 0.872362 in the original equation. If after the substitution, the left side of the original equation equals the right side of the original equation, 0.872362 is a solution.

Since the left side of the original equation equals the right side of the original equation after 0.872362 was substituted for x, then x=0.872362 is a solution.

You can also check the answer by graphing the equation:

displaymath69

The graph represents the right side of the original equation minus the left side of the original equation. There is only one x-intercept, at 0.872362, therefore 0.872362 is a solution to the equation.


If you would like to review the answer and solution to problem 2.3c, click on Solution.

If you would like to go back to the problem page, click on Problem.

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Author: Nancy Marcus

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