In each of these questions two equations numbered I and II are given. You have to solve both the equations and give answer
I. `x^2=25`
II. `y^2+10y+25=0`

Options

A. `xley`
B. `xgty`
C. `xgey`
D. the relationship can’t be established

Answer

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

### Step 1: Solve the first equation \( x^2 = 25 \)

1. To find the value of \( x \), we take the square root of both sides of the equation:
\[ x = \pm \sqrt{25} \]
2. This gives us:
\[ x = 5 \quad \text{or} \quad x = -5 \]

### Step 2: Solve the second equation \( y^2 + 10y + 25 = 0 \)

1. We can factor the quadratic equation. Notice that \( y^2 + 10y + 25 \) can be rewritten as:
\[ (y + 5)(y + 5) = 0 \]
or
\[ (y + 5)^2 = 0 \]
2. Setting the factor equal to zero gives us:
\[ y + 5 = 0 \]
3. Solving for \( y \) gives:
\[ y = -5 \]

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

1. From Step 1, we have two possible values for \( x \): \( 5 \) and \( -5 \).
2. From Step 2, we have one value for \( y \): \( -5 \).
3. We can now compare the values:
- When \( x = 5 \) and \( y = -5 \), we find that \( x > y \).
- When \( x = -5 \) and \( y = -5 \), we find that \( x = y \).

### Conclusion

Thus, the relationship between \( x \) and \( y \) is:
\[ x \geq y \]

### Final Answer

The correct answer is \( x \geq y \).

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