I. ` x = (1024)^(1//2)`
II. ` y^(2) = 1024`

Options

A. if` x gt y`
B. if ` x lt y`
C. if ` x le y`
D. if ` x ge y`

Explanation

To solve the equations given in the question, we will find the values of \( x \) and \( y \) step by step.

### Step 1: Solve for \( x \)
We start with the equation:
\[ x = (1024)^{\frac{1}{2}} \]

To simplify this, we can calculate the square root of 1024.

\[ 1024 = 32^2 \]
Thus,
\[ x = (32^2)^{\frac{1}{2}} = 32 \]

### Step 2: Solve for \( y \)
Next, we have the equation:
\[ y^2 = 1024 \]

To find \( y \), we take the square root of both sides:
\[ y = \pm \sqrt{1024} \]

Since we know \( 1024 = 32^2 \), we can write:
\[ y = \pm 32 \]

This means:
\[ y = 32 \quad \text{or} \quad y = -32 \]

### Step 3: Compare \( x \) and \( y \)
Now we have the values:
- \( x = 32 \)
- \( y = 32 \) or \( y = -32 \)

We can compare these values:
1. When \( y = 32 \):
\[ x = y \]
2. When \( y = -32 \):
\[ x > y \]

### Conclusion
From the above comparisons, we can conclude that:
\[ x \geq y \]

### Final Answer
Thus, the relation between \( x \) and \( y \) is:
\[ x \geq y \]

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