EQUATIONS CONTAINING VARIABLES UNDER ONE OR MORE RADICALS

Note:


Problem2.7b         $\sqrt[4]{10x-19}+3=6$

Answer:        x=10

Solution:

Isolate the radical term.

\begin{eqnarray*}\sqrt[4]{10x-19} &=&3 \\
&& \\
&&
\end{eqnarray*}


Raise both sides of the equation to the 4th power..bf


\begin{eqnarray*}\left( \sqrt[4]{10x-19}\right) ^{4} &=&\left( 3\right) ^{4} \\ ...
...-19 &=&81 \\
&& \\
&& \\
10x &=&100 \\
&& \\
&& \\
x &=&10
\end{eqnarray*}


Check your answer by substituting 10 in the original equation. If the left side of the original equation equals the right side of the original equation after the substitution, the answer 10

Left Side: $\qquad \sqrt[4]{10\left( 10\right) -19}+3=\sqrt[4]{81}+3=3+3=6$

Right Side$\qquad 6$

You can also check the answer by graphing the equation:

\begin{eqnarray*}y &=&\sqrt[4]{10x-19}-3 \\
&& \\
&&
\end{eqnarray*}


The graph represents the right side of the original equation minus the left side of the original equation.. Note that the x-intercept on the graph is located at 10, this confirms that 10 is our solution.


If you would like to go back to the problem page, 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