In each of the following questions, two equations (I) and (II) are given. Solve the equations and mark the correct option
I. ` x^(2) = 289 `
II. ` y = sqrt( 289)`

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 and find the relationship between \( x \) and \( y \), we will follow these steps:

### Step 1: Solve the first equation \( x^2 = 289 \)

1. Start with the equation:
\[ x^2 = 289 \]
2. Take the square root of both sides:
\[ x = \pm \sqrt{289} \]
3. Since \( 289 = 17^2 \), we can simplify:
\[ x = \pm 17 \]
4. Therefore, the possible values for \( x \) are:
\[ x = 17 \quad \text{or} \quad x = -17 \]

### Step 2: Solve the second equation \( y = \sqrt{289} \)

1. Start with the equation:
\[ y = \sqrt{289} \]
2. Since \( 289 = 17^2 \), we can simplify:
\[ y = 17 \]

### Step 3: Compare the values of \( x \) and \( y \)

1. We have two possible values for \( x \):
- \( x = 17 \)
- \( x = -17 \)

2. Now, we compare these values with \( y = 17 \):
- For \( x = 17 \):
\[ x = y \]
- For \( x = -17 \):
\[ x < y \]

### Step 4: Combine the relationships

1. From the above comparisons, we can conclude:
- When \( x = 17 \), \( x \) is equal to \( y \).
- When \( x = -17 \), \( x \) is less than \( y \).

2. Therefore, the overall relationship can be expressed as:
\[ x \leq y \]

### Final Answer

The correct option is:
\[ x \leq y \]

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