If `a o+ b = a^3 + b^2 + 1`
`a © b = (a - b)^2 + 1`
`a ** b = a^3 - b^2 + 1`
The value of `P = (((2 o+ 2) © 2)` is :

Options

A. 14441
B. 14401
C. 144001
D. None of these

Answer

To solve the problem step by step, we will evaluate the expression \( P = (((2 \, o+ \, 2) \, © \, 2) \).

### Step 1: Calculate \( 2 \, o+ \, 2 \)
Using the operator \( o+ \):
\[ a \, o+ \, b = a^3 + b^2 + 1 \]
Substituting \( a = 2 \) and \( b = 2 \):
\[ 2 \, o+ \, 2 = 2^3 + 2^2 + 1 \]
Calculating each term:
\[ 2^3 = 8, \quad 2^2 = 4 \]
Now, substituting these values:
\[ 2 \, o+ \, 2 = 8 + 4 + 1 = 13 \]

### Step 2: Calculate \( 13 \, © \, 2 \)
Now we need to calculate \( 13 \, © \, 2 \) using the operator \( © \):
\[ a \, © \, b = (a - b)^2 + 1 \]
Substituting \( a = 13 \) and \( b = 2 \):
\[ 13 \, © \, 2 = (13 - 2)^2 + 1 \]
Calculating the difference:
\[ 13 - 2 = 11 \]
Now squaring that:
\[ 11^2 = 121 \]
Finally, adding 1:
\[ 13 \, © \, 2 = 121 + 1 = 122 \]

### Final Answer
Thus, the value of \( P \) is:
\[ P = 122 \]

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