The original question does not make logical sense because the equations are incorrect. Here is a revised version that makes sense:

Solve for the missing value in the pattern:

[tex]\[
\begin{array}{ll}
6 + 1 = 7 & 3 + 4 = 7 \\
4 + 5 = 9 & 8 + 2 = ?
\end{array}
\][/tex]



Answer :

To determine the result of [tex]\(8 + 2\)[/tex] based on the given patterns in the equations, we need to analyze the provided equations and determine the pattern used to find the answers.

The equations given are:
1. [tex]\(6 + 1 = 6\)[/tex]
2. [tex]\(3 + 4 = 5\)[/tex]
3. [tex]\(4 + 5 = 6\)[/tex]

Let's try to recognize a pattern in each of these equations.

1. Consider the first equation: [tex]\(6 + 1 = 6\)[/tex].
It seems that instead of the usual arithmetic result of [tex]\(7\)[/tex], the given result is [tex]\(6\)[/tex]. One possible observation is that the result is the maximum of the two numbers.

2. Consider the second equation: [tex]\(3 + 4 = 5\)[/tex].
Here, instead of the usual arithmetic result of [tex]\(7\)[/tex], we get [tex]\(5\)[/tex]. It appears that [tex]\(5\)[/tex] is not directly the maximum of [tex]\(3\)[/tex] and [tex]\(4\)[/tex].

3. Consider the third equation: [tex]\(4 + 5 = 6\)[/tex].
Here, the typical result would be [tex]\(9\)[/tex], but the given result is [tex]\(6\)[/tex].

Given this irregularity, let's see if there's a consistent way in which the unique results are produced. Observe that if we take the maximum number and then subtract the difference between the two numbers, we may get some idea of the pattern.

Let's re-examine this hypothesis:
1. [tex]\(6 + 1\)[/tex]:
- The maximum is [tex]\(6\)[/tex].
- The difference is [tex]\(6 - 1 = 5\)[/tex].
- Subtract the difference from the maximum: [tex]\(6 - 5 = 1\)[/tex].

2. [tex]\(3 + 4\)[/tex]:
- The maximum is [tex]\(4\)[/tex].
- The difference is [tex]\(4 - 3 = 1\)[/tex].
- Subtract the difference from the maximum: [tex]\(4 - 1 = 3\)[/tex].

3. [tex]\(4 + 5\)[/tex]:
- The maximum is [tex]\(5\)[/tex].
- The difference is [tex]\(5 - 4 = 1\)[/tex].
- Subtract the difference from the maximum: [tex]\(5 - 1 = 4\)[/tex].

Now apply the same logic to [tex]\(8 + 2\)[/tex]:
- The maximum is [tex]\(8\)[/tex].
- The difference is [tex]\(8 - 2 = 6\)[/tex].
- Subtract the difference from the maximum: [tex]\(8 - 6 = 2\)[/tex].

Thus, following the same pattern observed, the result for [tex]\(8 + 2\)[/tex] is [tex]\(2\)[/tex].