Two equations (I) and (II) are given in each question. On the basis of these equations you have to decide the relation between x and y and give answer
I. ` sqrt( 1225x) + sqrt(4900) = 0 `
II. ` (81)^((1)/(4)) y + (343)^((1)/(3)) = 0 `

Options

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

Answer

To solve the given problem, we will analyze both equations step by step.

### Step 1: Solve Equation I
The first equation is:
\[ \sqrt{1225x} + \sqrt{4900} = 0 \]
First, we simplify \(\sqrt{4900}\):
\[ \sqrt{4900} = 70 \]
So, the equation becomes:
\[ \sqrt{1225x} + 70 = 0 \]
Now, we can isolate \(\sqrt{1225x}\):
\[ \sqrt{1225x} = -70 \]
Since the square root of any real number cannot be negative, this equation has no solution in the real number system. Therefore, we conclude:
\[ \text{No real solution for } x. \]

### Step 2: Solve Equation II
The second equation is:
\[ (81)^{\frac{1}{4}} y + (343)^{\frac{1}{3}} = 0 \]
First, we simplify \((81)^{\frac{1}{4}}\):
\[ 81 = 3^4 \Rightarrow (81)^{\frac{1}{4}} = 3 \]
Next, we simplify \((343)^{\frac{1}{3}}\):
\[ 343 = 7^3 \Rightarrow (343)^{\frac{1}{3}} = 7 \]
Now substituting these values back into the equation gives:
\[ 3y + 7 = 0 \]
Isolating \(y\):
\[ 3y = -7 \Rightarrow y = -\frac{7}{3} \]

### Step 3: Compare \(x\) and \(y\)
From our findings:
- \(x\) has no real solution.
- \(y = -\frac{7}{3}\).

Since \(x\) does not exist in the real number system, we cannot establish a direct comparison between \(x\) and \(y\). However, if we consider \(x\) as undefined or non-existent, we can say that \(y\) is a negative value.

### Conclusion
Since \(x\) has no real value and \(y\) is negative, we cannot determine a traditional inequality relationship. However, if we were to express the relationship in terms of existence, we might say:
\[ \text{No relation can be established between } x \text{ and } y. \]