In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer
`x^2=81`
II `y^2-18y+81=0`

Options

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

Answer

To solve the given equations step by step, let's start with the first equation.

### Step 1: Solve the first equation \( x^2 = 81 \)

To find the value of \( x \), we take the square root of both sides:

\[ x = \sqrt{81} \]

Calculating the square root, we find:

\[ x = 9 \quad \text{or} \quad x = -9 \]

### Step 2: Solve the second equation \( y^2 - 18y + 81 = 0 \)

This is a quadratic equation in the standard form \( ay^2 + by + c = 0 \). We can factor this equation.

The equation can be rewritten as:

\[ y^2 - 9y - 9y + 81 = 0 \]

Grouping the terms, we can factor it as:

\[ (y - 9)(y - 9) = 0 \]

This gives us:

\[ y - 9 = 0 \]

Thus, we find:

\[ y = 9 \]

### Step 3: Compare the values of \( x \) and \( y \)

From Step 1, we have two possible values for \( x \): \( 9 \) and \( -9 \). From Step 2, we have \( y = 9 \).

Now we compare the values:

1. If \( x = 9 \), then \( x = y \).
2. If \( x = -9 \), then \( x < y \).

### Conclusion

Since \( x \) can be either \( 9 \) or \( -9 \), we conclude that:

- In the case where \( x = 9 \), \( x \) is equal to \( y \).
- In the case where \( x = -9 \), \( x \) is less than \( y \).

Thus, we can say that \( x \) is less than or equal to \( y \).

### Final Answer

The final answer is: \( x \leq y \).

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