If X*Y = `X^2 + Y^2 - XY` then 11*13 is

Options

A. 117
B. 147
C. 290
D. 433

Answer

To solve the problem where \( X * Y = X^2 + Y^2 - XY \) and we need to find \( 11 * 13 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the operation**: We are given the operation defined as \( X * Y = X^2 + Y^2 - XY \).

2. **Substitute the values**: We need to calculate \( 11 * 13 \). Here, \( X = 11 \) and \( Y = 13 \).

3. **Apply the operation**:
\[ 11 * 13 = 11^2 + 13^2 - 11 \times 13 \]

4. **Calculate \( 11^2 \)**:
\[ 11^2 = 121 \]

5. **Calculate \( 13^2 \)**:
\[ 13^2 = 169 \]

6. **Calculate \( 11 \times 13 \)**:
\[ 11 \times 13 = 143 \]

7. **Combine the results**:
\[ 11 * 13 = 121 + 169 - 143 \]

8. **Calculate \( 121 + 169 \)**:
\[ 121 + 169 = 290 \]

9. **Subtract \( 143 \) from \( 290 \)**:
\[ 290 - 143 = 147 \]

10. **Final Result**:
\[ 11 * 13 = 147 \]

### Conclusion:
The value of \( 11 * 13 \) is \( 147 \).