In the following questions two equations numbered I and II are given. You have to solve both the equations and Give answer
I. `x^(3)-371 =629` II. `y^(3)-543= 788`

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 equations, we will follow these steps:

### Step 1: Solve Equation I
The first equation is:
\[ x^3 - 371 = 629 \]

To isolate \( x^3 \), we will add 371 to both sides:
\[ x^3 = 629 + 371 \]

Calculating the right side:
\[ x^3 = 1000 \]

### Step 2: Find the value of \( x \)
Now, we need to find \( x \) by taking the cube root of both sides:
\[ x = \sqrt[3]{1000} \]
\[ x = 10 \]

### Step 3: Solve Equation II
The second equation is:
\[ y^3 - 543 = 788 \]

To isolate \( y^3 \), we will add 543 to both sides:
\[ y^3 = 788 + 543 \]

Calculating the right side:
\[ y^3 = 1331 \]

### Step 4: Find the value of \( y \)
Now, we need to find \( y \) by taking the cube root of both sides:
\[ y = \sqrt[3]{1331} \]
\[ y = 11 \]

### Step 5: Compare the values of \( x \) and \( y \)
Now we have:
- \( x = 10 \)
- \( y = 11 \)

To compare the two values:
Since \( 10 < 11 \), we can conclude that:
\[ y > x \]

### Final Answer
The relation between \( x \) and \( y \) is:
\[ y \geq x \]