Answer :

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]