Direction: In the following questions two equations numbered (I) and (II) are given. You have to solve both equations and Give answer
I. `p^2=9^2` II. `(q-8)^2=9`

Options

A. If `p gt q`
B. If `p ge q`
C. If `q gt p`
D. if `q ge p`

Answer

To solve the given equations, we will follow these steps:

### Step 1: Solve the first equation \( p^2 = 9^2 \)

1. Start with the equation:
\[ p^2 = 9^2 \]
2. Calculate \( 9^2 \):
\[ 9^2 = 81 \]
3. Now, rewrite the equation:
\[ p^2 = 81 \]
4. Take the square root of both sides:
\[ p = \sqrt{81} \quad \text{or} \quad p = -\sqrt{81} \]
5. Calculate the square roots:
\[ p = 9 \quad \text{or} \quad p = -9 \]

### Step 2: Solve the second equation \( (q - 8)^2 = 9 \)

1. Start with the equation:
\[ (q - 8)^2 = 9 \]
2. Take the square root of both sides:
\[ q - 8 = \sqrt{9} \quad \text{or} \quad q - 8 = -\sqrt{9} \]
3. Calculate the square roots:
\[ q - 8 = 3 \quad \text{or} \quad q - 8 = -3 \]
4. Solve for \( q \):
- For \( q - 8 = 3 \):
\[ q = 3 + 8 = 11 \]
- For \( q - 8 = -3 \):
\[ q = -3 + 8 = 5 \]

### Step 3: Compare the values of \( p \) and \( q \)

- Possible values of \( p \): \( 9 \) and \( -9 \)
- Possible values of \( q \): \( 11 \) and \( 5 \)

### Step 4: Determine the relationship between \( p \) and \( q \)

- If \( p = 9 \):
- Compare with \( q = 11 \): \( 9 < 11 \)
- Compare with \( q = 5 \): \( 9 > 5 \)

- If \( p = -9 \):
- Compare with \( q = 11 \): \( -9 < 11 \)
- Compare with \( q = 5 \): \( -9 < 5 \)

### Conclusion

From the comparisons:
- In both cases, \( p \) is less than \( q \) when \( q = 11 \) and \( p = 9 \).
- In the case of \( p = -9 \), \( p \) is still less than both possible values of \( q \).

Thus, we conclude that \( q \) is always greater than \( p \).

### Final Answer

**q is greater than p.**

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