3 $ 4 Pattern Analysis
The problem defines a mathematical operation '$' using the following examples:
3 $ 4 = 37
4 $ 5 = 61
We need to find the value of 5 $ 6 by identifying the common pattern.
Rule Derivation
Observe that each result can be obtained using:
[
a $ b = a2 + b2 + (a × b)
]
Let's verify the pattern with the given examples.
For 3 $ 4:
[
32 + 42 + (3 × 4)
]
[
= 9 + 16 + 12
]
[
= 37
]
So, the pattern correctly gives:
[
3 $ 4 = 37
]
For 4 $ 5:
[
42 + 52 + (4 × 5)
]
[
= 16 + 25 + 20
]
[
= 61
]
So, the pattern also correctly gives:
[
4 $ 5 = 61
]
Therefore, the rule is:
[
a $ b = a2 + b2 + ab
]
5 $ 6 Calculation
Now apply the same rule for (5 $ 6):
[
5 $ 6 = 52 + 62 + (5 × 6)
]
[
= 25 + 36 + 30
]
[
= 91
]
Therefore:
[
5 $ 6 = 91
]
Final Answer
Option 4: 91
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Important Questions from Coding Decoding Based on Numbers
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