EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS


Note::

Example 5: tex2html_wrap_inline123

Since the index of the radical is even, the quantity under the

radical cannot be negative and tex2html_wrap_inline125 .

Subtract 18 from both sides of the equation so that the radical

term is isolated.

tex2html_wrap_inline127

At this point you observe that the positive left side of the

equation cannot equal the negative number on the right side of the

equation, you are through. There is no solution. If you did not make

this observation, let's continue.

Divide both sides by 3 and then square both sides of the equation.

tex2html_wrap_inline129

(2x+9)=4

2x=-5

tex2html_wrap_inline135

The answer is tex2html_wrap_inline135

Check the solution by substituting tex2html_wrap_inline139 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.

Left side:

tex2html_wrap_inline143

tex2html_wrap_inline145

3*2+18

6+18

=24

Right side: Since the left side of the equation does not equal the right side of

the original equation when you substitute your answer, your answer is

not the solution. There is no solution.

You can also check the answer by graphing

tex2html_wrap_inline153

(the left side of the original equation minus the right side of the

original equation). The solution will be the x-intercept. There is no x-

intercept, and hence there is no solution.

If you would like to test yourself by working some problems similar to

this example, click on problem Links to S2211

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

here.



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