The sum of a number and its reciprocal is `2(1)/(30)`. Find the numbers.

Explanation

To solve the problem, we need to find a number \( A \) such that the sum of the number and its reciprocal equals \( \frac{2}{30} \).

### Step 1: Set up the equation
We start with the equation based on the problem statement:
\[ A + \frac{1}{A} = \frac{2}{30} \]

### Step 2: Simplify the right side
We can simplify \( \frac{2}{30} \) to \( \frac{1}{15} \):
\[ A + \frac{1}{A} = \frac{1}{15} \]

### Step 3: Multiply through by \( 15A \)
To eliminate the fraction, we multiply both sides of the equation by \( 15A \):
\[ 15A^2 + 15 = A \]

### Step 4: Rearrange the equation
Rearranging gives us a standard form of a quadratic equation:
\[ 15A^2 - A + 15 = 0 \]

### Step 5: Identify coefficients
Here, we identify the coefficients:
- \( a = 15 \)
- \( b = -1 \)
- \( c = 15 \)

### Step 6: Calculate the discriminant
We calculate the discriminant \( D \) using the formula \( D = b^2 - 4ac \):
\[ D = (-1)^2 - 4 \cdot 15 \cdot 15 = 1 - 900 = -899 \]

### Step 7: Analyze the discriminant
Since the discriminant is negative (\( D < 0 \)), this means that there are no real solutions for \( A \). Thus, there are no real numbers that satisfy the original equation.

### Conclusion
The conclusion is that there are no real numbers whose sum with their reciprocal equals \( \frac{2}{30} \).

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