If ` a^((1)/(3)) = 11 `, then the value of ` a^(2) - 331 a` is

Options

A. 1331331
B. 1331000
C. 1334331
D. 1330030

Answer

To solve the problem, we start with the equation given:

1. **Given Equation**:
\[ a^{\frac{1}{3}} = 11 \]

2. **Cubing Both Sides**:
To find the value of \( a \), we cube both sides of the equation:
\[ a = 11^3 \]

3. **Calculating \( 11^3 \)**:
We calculate \( 11^3 \):
\[ 11^3 = 11 \times 11 \times 11 = 121 \times 11 = 1331 \]
So, we have:
\[ a = 1331 \]

4. **Finding \( a^2 - 331a \)**:
Now, we need to find the value of \( a^2 - 331a \):
\[ a^2 - 331a = 1331^2 - 331 \times 1331 \]

5. **Calculating \( 1331^2 \)**:
We can calculate \( 1331^2 \) using the formula \( (x+y)^2 = x^2 + 2xy + y^2 \) or directly:
\[ 1331^2 = 1771561 \]

6. **Calculating \( 331 \times 1331 \)**:
Next, we calculate \( 331 \times 1331 \):
\[ 331 \times 1331 = 440561 \]

7. **Substituting Values**:
Now we substitute these values back into the equation:
\[ a^2 - 331a = 1771561 - 440561 \]

8. **Final Calculation**:
Performing the subtraction:
\[ 1771561 - 440561 = 1331000 \]

Thus, the final answer is:
\[ \boxed{1331000} \]