In the following question two equations are given in variables X and Y. You have to solve these equations and determine the relation between X and Y.
`x^2 – 16x + 64 = 0`
`Y^2 = 64`

Options

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

Explanation

To solve the given equations and determine the relation between X and Y, we will follow these steps:

### Step 1: Solve the first equation for X.
The first equation is:
\[ x^2 - 16x + 64 = 0 \]

This is a quadratic equation. We can factor it:
\[ (x - 8)(x - 8) = 0 \]
or
\[ (x - 8)^2 = 0 \]

Setting the factor equal to zero gives us:
\[ x - 8 = 0 \]
Thus,
\[ x = 8 \]

### Step 2: Solve the second equation for Y.
The second equation is:
\[ Y^2 = 64 \]

To find Y, we take the square root of both sides:
\[ Y = \sqrt{64} \]
This gives us two possible values for Y:
\[ Y = 8 \quad \text{or} \quad Y = -8 \]

### Step 3: Determine the relationship between X and Y.
From Step 1, we found that:
\[ X = 8 \]

From Step 2, we found that:
\[ Y = 8 \quad \text{or} \quad Y = -8 \]

Now, we can compare the values:
- When \( Y = 8 \), \( X = Y \).
- When \( Y = -8 \), \( X > Y \) (since \( 8 > -8 \)).

### Conclusion:
The relationship between X and Y can be summarized as:
- \( X \geq Y \)