Solve the given quadratic equations and mark the correct option based on your answer
I. ` x^(2) = 144`
II. ` ( y + 12) ^(2) = 0 `

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 quadratic equations, we will follow these steps:

### Step 1: Solve the first equation \( x^2 = 144 \)

1. **Rearranging the equation**:
\[ x^2 - 144 = 0 \]

2. **Factoring the equation**:
This can be factored using the difference of squares:
\[ (x - 12)(x + 12) = 0 \]

3. **Finding the values of \( x \)**:
Set each factor to zero:
\[ x - 12 = 0 \quad \Rightarrow \quad x = 12 \]
\[ x + 12 = 0 \quad \Rightarrow \quad x = -12 \]

### Step 2: Solve the second equation \( (y + 12)^2 = 0 \)

1. **Taking the square root**:
Since the square of a number is zero only when the number itself is zero:
\[ y + 12 = 0 \]

2. **Finding the value of \( y \)**:
\[ y = -12 \]

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

1. **Values obtained**:
- From the first equation, we have \( x = 12 \) and \( x = -12 \).
- From the second equation, we have \( y = -12 \).

2. **Comparison**:
- Compare \( x = 12 \) with \( y = -12 \):
\[ 12 > -12 \]
- Compare \( x = -12 \) with \( y = -12 \):
\[ -12 = -12 \]

### Conclusion:

- The values of \( x \) are \( 12 \) and \( -12 \).
- The value of \( y \) is \( -12 \).
- Thus, we can conclude:
\[ x \geq y \]

### Final Answer:
The correct option based on the comparison is **Option B: \( x \geq y \)**.

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