If a ~ b = a2 + b, a ^ b = b+ a, find (3 ∼ 6) ^ 2.

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  1. 18
  2. 23
  3. 19
  4. 21

Answer (Detailed Solution Below)

Option 3 : 19
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Detailed Solution

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Given:

a ~ b = a2 + b, and a ^ b = b2 + a.

We are asked to find (3 ~ 6) ^ 2.

Calculation:

Calculate 3 ~ 6

From the given definition of a ~ b, we have:

3 ~ 6 = 32 + 6 = 9 + 6 = 15.

Calculate (3 ~ 6) ^ 2

Now, using the definition of a ^ b, we have:

(3 ~ 6) ^ 2 = 15 ^ 2 = 22 + 15 = 4 + 15 = 19.

∴ (3 ~ 6) ^ 2 = 19.

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