In each of the following questions, two equations (I) and (II) are given . Solve the equations and mark the correct options :
I. ` x^(2) + 215 = 1176`
II. ` y = sqrt( 961)`

Options

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

Answer

To solve the given equations step by step, we will analyze each equation separately and then compare the results.

### Step 1: Solve the first equation
The first equation is:
\[ x^2 + 215 = 1176 \]

To isolate \( x^2 \), we will subtract 215 from both sides:
\[ x^2 = 1176 - 215 \]

Calculating the right side:
\[ x^2 = 961 \]

### Step 2: Take the square root
Next, we will take the square root of both sides to find \( x \):
\[ x = \pm \sqrt{961} \]

Calculating the square root:
\[ x = \pm 31 \]

Thus, the possible values for \( x \) are:
\[ x = 31 \quad \text{or} \quad x = -31 \]

### Step 3: Solve the second equation
The second equation is:
\[ y = \sqrt{961} \]

Calculating the square root:
\[ y = 31 \]

### Step 4: Compare the values of \( x \) and \( y \)
Now we have:
- \( x = 31 \) or \( x = -31 \)
- \( y = 31 \)

We can compare the values:
1. If \( x = 31 \), then \( x = y \).
2. If \( x = -31 \), then \( x < y \).

### Step 5: Conclusion
From the above comparisons, we can conclude that:
\[ x \leq y \]

### Final Answer
The correct relation is:
\[ x \leq y \]