EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Example 4:.         $\sqrt[5]{2x+3}+7=8$

Isolate the radical term

\begin{eqnarray*}&&\\
\sqrt[5]{2x+3} &=&1 \\
&&
\end{eqnarray*}


Raise both sides of the equation to the power 5 and simplify.


\begin{eqnarray*}\left( \sqrt[5]{2x+3}\right) ^{5} &=&\left( 1\right) ^{5} \\
&...
...
&& \\
&& \\
2x &=&-2 \\
&& \\
&& \\
x &=&-1 \\
&& \\
&&
\end{eqnarray*}


The answer is x=-1

Check the solution by substituting -1 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:         $\sqrt[5]{2\left( -1\right) +3}+7=1+7=8$

Right Side:        8

Since the left side of the original equation equals the right side of the original equation after you substitute -1 for x, then -1 is a solution.

You can also check your solution by graphing the function

\begin{eqnarray*}f(x) &=&\sqrt[5]{2x+3}-1 \\
&& \\
&&
\end{eqnarray*}


The above function is formed by subtracting the right side of the original equation from the left side of the original equation. The x-intercept of the graph is the solution to the original equation. As you can see, there is one x-intercept at -1. We have verified our solutions graphically.

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.


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Author:Nancy Marcus

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