In each of these questions, two equations (I) and (II) are given . You have to solve both the equations and give answer
I. ` x^(3) - 468 = 1729`
II. ` y^(2) - 1733 + 1564 = 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 first address each equation separately.

### Step 1: Solve Equation I
The first equation is:
\[ x^3 - 468 = 1729 \]

**Step 1.1: Rearranging the equation**
To isolate \( x^3 \), we add 468 to both sides:
\[ x^3 = 1729 + 468 \]

**Step 1.2: Performing the addition**
Now, we calculate the right side:
\[ x^3 = 2197 \]

**Step 1.3: Taking the cube root**
Next, we find the cube root of both sides:
\[ x = \sqrt[3]{2197} \]

Since \( 2197 = 13^3 \):
\[ x = 13 \]

### Step 2: Solve Equation II
The second equation is:
\[ y^2 - 1733 + 1564 = 0 \]

**Step 2.1: Simplifying the equation**
First, we simplify the equation:
\[ y^2 - (1733 - 1564) = 0 \]
\[ y^2 - 169 = 0 \]

**Step 2.2: Rearranging the equation**
Now, we can rearrange it to isolate \( y^2 \):
\[ y^2 = 169 \]

**Step 2.3: Taking the square root**
Next, we take the square root of both sides:
\[ y = \pm \sqrt{169} \]
\[ y = \pm 13 \]

### Summary of Solutions
From the above steps, we have:
- \( x = 13 \)
- \( y = 13 \) or \( y = -13 \)

### Step 3: Analyzing the relationship between x and y
Now, we compare the values of \( x \) and \( y \):
- If \( y = 13 \), then \( x = y \).
- If \( y = -13 \), then \( x > y \) since \( 13 > -13 \).

Thus, we can conclude that:
\[ x \geq y \]

### Final Answer
The relationship can be expressed as:
\[ x \geq y \]