In the following questions, two equations numbered I and II are given. You have to solve both the equations and
I `x^2+8x+15=0`
II. `y^2`=49

Options

A. `xgty`
B. `x le y`
C. `x ge y`
D. the relationship cannot be established

Answer

To solve the given equations step by step, we will handle each equation separately.

### Step 1: Solve the first equation \(x^2 + 8x + 15 = 0\)

1. **Identify the coefficients**: The equation is in the standard form \(ax^2 + bx + c = 0\), where \(a = 1\), \(b = 8\), and \(c = 15\).

2. **Factor the quadratic**: We need to find two numbers that multiply to \(c\) (15) and add up to \(b\) (8). The numbers 3 and 5 satisfy this condition because:
- \(3 \times 5 = 15\)
- \(3 + 5 = 8\)

3. **Write the factored form**: The equation can be factored as:
\[ (x + 3)(x + 5) = 0 \]

4. **Set each factor to zero**:
- \(x + 3 = 0 \Rightarrow x = -3\)
- \(x + 5 = 0 \Rightarrow x = -5\)

5. **Solutions for x**: Thus, the solutions for \(x\) are:
\[ x = -3 \quad \text{and} \quad x = -5 \]

### Step 2: Solve the second equation \(y^2 = 49\)

1. **Take the square root**: To solve for \(y\), take the square root of both sides:
\[ y = \pm \sqrt{49} \]

2. **Calculate the square root**: The square root of 49 is 7, so:
\[ y = 7 \quad \text{or} \quad y = -7 \]

3. **Solutions for y**: Thus, the solutions for \(y\) are:
\[ y = 7 \quad \text{and} \quad y = -7 \]

### Step 3: Compare the values of x and y

1. **List the values**: We have:
- \(x = -3\) and \(x = -5\)
- \(y = 7\) and \(y = -7\)

2. **Compare the values**:
- For \(x = -3\): \( -3 < 7 \) and \( -3 > -7 \)
- For \(x = -5\): \( -5 < 7 \) and \( -5 > -7 \)

### Conclusion

- The values of \(x\) are both less than \(y = 7\) and greater than \(y = -7\).
- Thus, there is no definitive relationship established between \(x\) and \(y\) that can be concluded as greater or lesser in a consistent manner.

### Final Answer

The correct answer is that there is no relationship between \(x\) and \(y\).

---