Sure! Let's carefully analyze the table and find the missing value [tex]\( x \)[/tex].
Here is the table given:
[tex]\[
\begin{array}{|l|l|l|}
\hline
1 & 1 & 2 \\
\hline
2 & 4 & 4 \\
\hline
3 & x & 6 \\
\hline
\end{array}
\][/tex]
We will analyze column by column and identify any patterns or relationships.
1. First Column: The numbers in the first column are 1, 2, and 3. This column appears to be a simple sequence of natural numbers.
2. Second Column: The numbers in this column are 1, 4, and [tex]\( x \)[/tex]. Let's look for a pattern:
- The first entry in the second column is 1, which is [tex]\( 1^2 \)[/tex].
- The second entry is 4, which is [tex]\( 2^2 \)[/tex].
From these observations, it appears that each number in the second column is the square of the corresponding number in the first column. Based on this:
- The missing entry [tex]\( x \)[/tex] corresponding to 3 in the first column should be [tex]\( 3^2 \)[/tex].
This gives:
[tex]\[ x = 3^2 = 9 \][/tex]
Therefore, the missing value [tex]\( x \)[/tex] is:
[tex]\[ \boxed{9} \][/tex]
