In each of these questions, two equations (I) and (II) are given. Solve the equations and mark the correct option
I. `x^(3) = 1331`
II. ` y = 3sqrt(1331)`

Options

A. ` x gt y `
B. ` x ge y `
C. ` x lt y `
D. x = y or relation cat't be established

Answer

To solve the given equations and determine the relationship between \( x \) and \( y \), we will follow these steps:

### Step 1: Solve Equation I
The first equation is:
\[ x^3 = 1331 \]

To find \( x \), we take the cube root of both sides:
\[ x = \sqrt[3]{1331} \]

### Step 2: Calculate the Cube Root
Now, we need to calculate \( \sqrt[3]{1331} \). We can do this by recognizing that:
\[ 11^3 = 11 \times 11 \times 11 = 121 \times 11 = 1331 \]

Thus, we find:
\[ x = 11 \]

### Step 3: Solve Equation II
The second equation is:
\[ y = 3\sqrt{1331} \]

Now, we need to calculate \( \sqrt{1331} \). Since we already know \( 1331 = 11^3 \), we can express it as:
\[ \sqrt{1331} = \sqrt{11^3} = 11\sqrt{11} \]

Now substituting this back into the equation for \( y \):
\[ y = 3 \times 11\sqrt{11} = 33\sqrt{11} \]

### Step 4: Compare \( x \) and \( y \)
Now we have:
- \( x = 11 \)
- \( y = 33\sqrt{11} \)

To compare \( x \) and \( y \), we need to evaluate \( 33\sqrt{11} \):
Since \( \sqrt{11} \) is approximately \( 3.316 \):
\[ y \approx 33 \times 3.316 \approx 109.428 \]

Now, we compare:
- \( x = 11 \)
- \( y \approx 109.428 \)

Clearly, \( y > x \).

### Conclusion
Thus, we can conclude:
- \( x < y \)

### Final Answer
The relationship between \( x \) and \( y \) is that \( x < y \).

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