In the following questions, two equations numbered I and II are given. You have to solve both the equations and
Give answer If
`(x+13)^2=0`
`y^2+y-56=0`

Options

A. `xlty`
B. `xgty`
C. `xley`
D. `xgey`

Answer

To solve the given equations step by step, we will follow these steps:

### Step 1: Solve the first equation
The first equation is:
\[ (x + 13)^2 = 0 \]
To solve for \(x\), we take the square root of both sides:
\[ x + 13 = 0 \]
Now, isolate \(x\) by subtracting 13 from both sides:
\[ x = -13 \]

### Step 2: Solve the second equation
The second equation is:
\[ y^2 + y - 56 = 0 \]
To solve for \(y\), we can factor the quadratic equation. We need to find two numbers that multiply to \(-56\) and add to \(1\) (the coefficient of \(y\)). The numbers \(8\) and \(-7\) satisfy this condition:
\[ y^2 + 8y - 7y - 56 = 0 \]
Now, we can group the terms:
\[ (y + 8)(y - 7) = 0 \]
Setting each factor to zero gives us:
\[ y + 8 = 0 \quad \text{or} \quad y - 7 = 0 \]
From \(y + 8 = 0\):
\[ y = -8 \]
From \(y - 7 = 0\):
\[ y = 7 \]

### Step 3: Compare the values of \(x\) and \(y\)
Now we have:
- \(x = -13\)
- \(y = 7\) or \(y = -8\)

We will compare \(x\) with both values of \(y\):
1. When \(y = 7\):
\[ -13 < 7 \quad \text{(True)} \]
2. When \(y = -8\):
\[ -13 < -8 \quad \text{(True)} \]

In both cases, we find that \(x < y\).

### Final Conclusion
Thus, the relationship between \(x\) and \(y\) is:
\[ x < y \]