In each question two equations numbered (I) and (II) are given . You have to solve both the equations and mark appropriate answer
I. ` x^(2) = 81 `
II. ` y^(2) = 64`

Options

A. If x= y or no relation
B. If ` x gt y `
C. If ` x lt y `
D. If `x ge y`

Answer

To solve the given equations and compare the values of \(x\) and \(y\), we will follow these steps:

### Step 1: Solve Equation I
The first equation is:
\[ x^2 = 81 \]
To solve for \(x\), we take the square root of both sides:
\[ x = \pm \sqrt{81} \]
Calculating the square root:
\[ x = \pm 9 \]
Thus, the possible values for \(x\) are:
\[ x = 9 \quad \text{and} \quad x = -9 \]

### Step 2: Solve Equation II
The second equation is:
\[ y^2 = 64 \]
To solve for \(y\), we take the square root of both sides:
\[ y = \pm \sqrt{64} \]
Calculating the square root:
\[ y = \pm 8 \]
Thus, the possible values for \(y\) are:
\[ y = 8 \quad \text{and} \quad y = -8 \]

### Step 3: Compare the Values of \(x\) and \(y\)
Now we have the values:
- For \(x\): \(9\) and \(-9\)
- For \(y\): \(8\) and \(-8\)

We will compare these values:
1. Compare \(9\) and \(8\):
\[ 9 > 8 \quad \text{(True)} \]
2. Compare \(9\) and \(-8\):
\[ 9 > -8 \quad \text{(True)} \]
3. Compare \(-9\) and \(8\):
\[ -9 < 8 \quad \text{(True)} \]
4. Compare \(-9\) and \(-8\):
\[ -9 < -8 \quad \text{(True)} \]

### Conclusion
From the comparisons:
- \(9 > 8\)
- \(9 > -8\)
- \(-9 < 8\)
- \(-9 < -8\)

Since we have both greater and lesser relationships, we can conclude that there is no consistent relationship between \(x\) and \(y\). Therefore, the answer is:
\[ \text{No relation} \]