In each of the following questions, two equations are given. You have to solve them
`"I. "x^3-2314=2599" II. "y^2-1733+1564=0`

Options

A. `xgty`
B. `xgey`
C. `xlty`
D. `xley`

Answer

To solve the given equations step by step, let's break it down:

### Step 1: Solve the first equation
The first equation is:
\[ x^3 - 2314 = 2599 \]

To isolate \( x^3 \), we add 2314 to both sides:
\[ x^3 = 2599 + 2314 \]

Calculating the right side:
\[ x^3 = 4913 \]

### Step 2: Find the value of \( x \)
Now, we need to find \( x \) by taking the cube root of both sides:
\[ x = \sqrt[3]{4913} \]

Calculating the cube root:
\[ x = 17 \]

### Step 3: Solve the second equation
The second equation is:
\[ y^2 - 1733 + 1564 = 0 \]

First, simplify the equation by combining like terms:
\[ y^2 - 1733 + 1564 = y^2 - 169 = 0 \]

### Step 4: Factor the equation
Now, we can factor the equation:
\[ y^2 - 169 = 0 \]

This can be factored as:
\[ (y - 13)(y + 13) = 0 \]

### Step 5: Find the values of \( y \)
Setting each factor to zero gives us:
1. \( y - 13 = 0 \) → \( y = 13 \)
2. \( y + 13 = 0 \) → \( y = -13 \)

### Step 6: Compare the values of \( x \) and \( y \)
Now we have:
- \( x = 17 \)
- \( y = 13 \) or \( y = -13 \)

Since \( 17 \) is greater than both \( 13 \) and \( -13 \), we can conclude:
\[ x > y \]

### Final Answer
Thus, the answer is that \( x \) is always greater than \( y \).

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