Given the following equation:
[tex]\text{ }\sqrt{3x\text{ + 12}}\text{ = 9}[/tex]
Let's solve for x,
[tex]\text{ }\sqrt{3x\text{ + 12}}\text{ = 9}[/tex][tex]\text{ \lparen}\sqrt{3x\text{ + 12}})^2\text{ = \lparen9\rparen}^2\text{ }[/tex][tex]\text{ 3x + 12 = 81}[/tex][tex]\text{ 3x = 81 - 12}[/tex][tex]\text{ 3x = 69}[/tex][tex]\text{ }\frac{\text{ 3x }}{\text{ 3 }}\text{ = }\frac{\text{ 69 }}{\text{ 3 }}[/tex][tex]\text{ x = 23}[/tex]
Therefore, x = 23
In mathematics, an extraneous solution (or spurious solution) is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem.
To check if the solution is extraneous, plug in x = 23 in the equation.
[tex]\begin{gathered} \text{ }\sqrt{3x\text{ + 12}}\text{ = 9} \\ \text{ }\sqrt{3(23)\text{ + 12}}\text{ = 9} \\ \text{ }\sqrt{69\text{ + 12}}\text{ = 9} \\ \text{ }\sqrt{81}\text{ = 9} \\ \text{ 9 = 9 \lparen True\rparen} \end{gathered}[/tex]
The solution is, therefore, not extraneous.
