I. ` (x)^(2) = 961" "` II. ` y = sqrt(961) `

Options

A. if ` x gt y`
B. if `x ge y`
C. if ` x lt y`
D. if x = y or the relationship cannot be established

Explanation

To solve the equations given in the question, we will follow these steps:

### Step 1: Solve for x in the equation \( x^2 = 961 \)

To find the value of \( x \), we take the square root of both sides of the equation:

\[ x = \pm \sqrt{961} \]

### Step 2: Calculate \( \sqrt{961} \)

Now, we need to calculate the square root of 961. We know that:

\[ \sqrt{961} = 31 \]

Thus, we can express \( x \) as:

\[ x = \pm 31 \]

### Step 3: Solve for y in the equation \( y = \sqrt{961} \)

Next, we solve for \( y \):

\[ y = \sqrt{961} \]

From our previous calculation, we know:

\[ y = 31 \]

### Step 4: Establish the relationship between x and y

Now we have two values for \( x \):

\[ x = 31 \quad \text{or} \quad x = -31 \]

And we have:

\[ y = 31 \]

This means that \( x \) can either be equal to \( y \) or \( x \) can be the negative of \( y \). Therefore, we can conclude:

\[ x = y \quad \text{or} \quad x = -y \]

### Final Conclusion

The relationship between \( x \) and \( y \) can be summarized as:

\[ x = y \quad \text{or} \quad x = -y \]

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