Read the given question and decide which of the following equation is /are sufficient to answer the question.
Question:
What is the value of x?
Equations:
1) `x^2-18x+81=0`
2) `P+q+r=0`
A)Only 1 is sufficient.
B)Either 1 or 2 is sufficient.
C)Neither 1 nor 2 is sufficient.
D)Only 2 is sufficient.

Options

A. Only 1 is sufficient.
B. Either 1 or 2 is sufficient.
C. Neither 1 nor 2 is sufficient.
D. Only 2 is sufficient.

Answer

To determine the value of \( x \) from the given equations, we will analyze each equation step by step.

### Step 1: Analyze Equation 1
The first equation provided is:
\[ x^2 - 18x + 81 = 0 \]

This is a quadratic equation in standard form \( ax^2 + bx + c = 0 \), where:
- \( a = 1 \)
- \( b = -18 \)
- \( c = 81 \)

### Step 2: Factor the Quadratic Equation
To solve the equation, we can factor it. We need to find two numbers that multiply to \( c \) (which is 81) and add up to \( b \) (which is -18).

The numbers that satisfy this are:
- \( -9 \) and \( -9 \) (since \( -9 \times -9 = 81 \) and \( -9 + -9 = -18 \))

Thus, we can factor the equation as:
\[ (x - 9)(x - 9) = 0 \]
or simply:
\[ (x - 9)^2 = 0 \]

### Step 3: Solve for \( x \)
Setting the factored equation to zero gives:
\[ x - 9 = 0 \]
Thus, solving for \( x \) yields:
\[ x = 9 \]

### Step 4: Analyze Equation 2
The second equation provided is:
\[ P + Q + R = 0 \]

This equation does not contain the variable \( x \) and does not provide any information about \( x \). Therefore, it is not sufficient to determine the value of \( x \).

### Conclusion
From the analysis:
- Equation 1 is sufficient to find the value of \( x \) (which is 9).
- Equation 2 is not sufficient to find \( x \).

Thus, the correct answer is:
**A) Only 1 is sufficient.**

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