#### EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:

- In order to solve for x, you must isolate x.
- In order to isolate x, you must remove it from under the radial.
- If there is just one radical in the equation, isolate the radical.
- Then raise both sides of the equation to a power equal to the index
of the radical.
- With these types of equations, sometimes there are extraneous
solutions; therefore, you must check your answers.
- If the index of the radical is even, many times there will be a
restriction on the values of x.

Problem2.6b:

Answer: 79

Solution:

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

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

Raise both sides of the equation to the fourth power.

You can check the solution by substituting the value 79 in the original equation.
If, after the substitution, the left side of the original equation equals the right side of the
original equation, 79 is the verified solution.

You can also check the answer by graphing the equation:

The graph represents the right side of the original equation minus the left
side of the original equation. From the graph you can see that there
is one x-intercept located at 79. This verifies that 79 is the solution.

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