I. ` sqrt(1225 x^(2))+sqrt(4900) = 0`
II. ` (81)^(1//4) y + (343)^(1//3) = 0`

Options

A. if`x gt y`
B. if `x ge y`
C. if `x lt y`
D. if `x le y`

Explanation

To solve the given equations step by step, we will start with the first equation and then move on to the second equation.

### Step 1: Solve the first equation
Given:
\[ \sqrt{1225 x^2} + \sqrt{4900} = 0 \]

First, we simplify each square root:
- \( \sqrt{1225} = 35 \)
- \( \sqrt{4900} = 70 \)

Now, substituting these values back into the equation:
\[ 35 |x| + 70 = 0 \]

### Step 2: Isolate the absolute value
To isolate the absolute value term, we can move \( 70 \) to the other side:
\[ 35 |x| = -70 \]

### Step 3: Analyze the equation
Since \( 35 |x| \) is always non-negative (as absolute values are non-negative), it can never equal a negative number (-70). Therefore, there are no real solutions for \( x \) in this equation.

### Step 4: Solve the second equation
Now, let's solve the second equation:
\[ (81)^{1/4} y + (343)^{1/3} = 0 \]

First, we simplify each term:
- \( (81)^{1/4} = 3 \) because \( 81 = 3^4 \)
- \( (343)^{1/3} = 7 \) because \( 343 = 7^3 \)

Substituting these values back into the equation:
\[ 3y + 7 = 0 \]

### Step 5: Isolate \( y \)
Now, isolate \( y \):
\[ 3y = -7 \]
\[ y = -\frac{7}{3} \]

### Step 6: Relation between \( x \) and \( y \)
From the first equation, we found that there are no real solutions for \( x \), and from the second equation, we found:
\[ y = -\frac{7}{3} \approx -2.33 \]

Since \( x \) has no real solution, we cannot establish a direct numerical relation between \( x \) and \( y \). However, we can state that since \( x \) has no real value, any comparison with \( y \) is not applicable.

### Summary of Solutions:
- For the first equation, there are no real solutions for \( x \).
- For the second equation, \( y = -\frac{7}{3} \).