The sum and product of two numbers are - 2 and - 63 respectively. The sum of their reciprocals is

Options

A. `(-2)/63`
B. `2/63`
C. `16/63`
D. `(-2)/9`

Answer

To solve the problem, we need to find the sum of the reciprocals of two numbers given their sum and product. Let's denote the two numbers as \( x \) and \( y \).

### Step 1: Write down the given information
We know:
- The sum of the two numbers:
\[ x + y = -2 \]
- The product of the two numbers:
\[ x \cdot y = -63 \]

### Step 2: Write the formula for the sum of the reciprocals
The sum of the reciprocals of \( x \) and \( y \) can be expressed as:
\[ \frac{1}{x} + \frac{1}{y} = \frac{y + x}{xy} \]

### Step 3: Substitute the known values
From Step 1, we know that \( x + y = -2 \) and \( x \cdot y = -63 \). We can substitute these values into the formula from Step 2:
\[ \frac{1}{x} + \frac{1}{y} = \frac{x + y}{x \cdot y} = \frac{-2}{-63} \]

### Step 4: Simplify the expression
Now we simplify the fraction:
\[ \frac{-2}{-63} = \frac{2}{63} \]

### Final Answer
Thus, the sum of the reciprocals of the two numbers is:
\[ \frac{2}{63} \]