If a * b `= a^(2) + b^(2)` and `a.b = a^(2) - b^(2)`, then the value of (5 * 2).25 is

Options

A. 225
B. 226
C. 216
D. 215

Answer

To solve the problem step by step, we will use the definitions provided for the operations \( * \) and \( . \).

### Step 1: Calculate \( 5 * 2 \)
According to the definition given, \( a * b = a^2 + b^2 \).

So, we calculate:
\[ 5 * 2 = 5^2 + 2^2 \]
Calculating the squares:
\[ 5^2 = 25 \quad \text{and} \quad 2^2 = 4 \]
Now, add these results:
\[ 5 * 2 = 25 + 4 = 29 \]

### Step 2: Calculate \( 29 . 25 \)
Now we need to calculate \( 29 . 25 \) using the definition \( a . b = a^2 - b^2 \).

So, we calculate:
\[ 29 . 25 = 29^2 - 25^2 \]
Calculating the squares:
\[ 29^2 = 841 \quad \text{and} \quad 25^2 = 625 \]
Now, subtract these results:
\[ 29 . 25 = 841 - 625 = 216 \]

### Final Answer
Thus, the value of \( (5 * 2) . 25 \) is \( 216 \).

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