In each of these questions, two equations (I) and (II) are given . You have to solve both the equations and give answer
I. ` x^(2) + 4 x + 4 = 0 `
II. ` y^(2) + 8y + 16 = 0 `

Options

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

Answer

To solve the given equations step by step, we will start with the first equation and then move on to the second equation.

### Step 1: Solve Equation I
The first equation is:
\[ x^2 + 4x + 4 = 0 \]

This can be factored as:
\[ (x + 2)(x + 2) = 0 \]
or
\[ (x + 2)^2 = 0 \]

Setting the factor equal to zero gives:
\[ x + 2 = 0 \]
Thus,
\[ x = -2 \]

### Step 2: Solve Equation II
The second equation is:
\[ y^2 + 8y + 16 = 0 \]

This can also be factored as:
\[ (y + 4)(y + 4) = 0 \]
or
\[ (y + 4)^2 = 0 \]

Setting the factor equal to zero gives:
\[ y + 4 = 0 \]
Thus,
\[ y = -4 \]

### Step 3: Compare the Values of x and y
Now we have:
- \( x = -2 \)
- \( y = -4 \)

To compare \( x \) and \( y \):
Since \( -2 \) is greater than \( -4 \), we conclude:
\[ x > y \]

### Final Answer
Thus, the relation between \( x \) and \( y \) is:
\[ x \text{ is greater than } y \]

---