The sum of three numbers in HP is 37 and the sum of their reciprocals is `(1)/(4)`. Find the numbers.

Explanation

To solve the problem, we need to find three numbers in Harmonic Progression (HP) given that their sum is 37 and the sum of their reciprocals is \( \frac{1}{4} \).

### Step 1: Understanding Harmonic Progression
In HP, the reciprocals of the numbers are in Arithmetic Progression (AP). Let's denote the three numbers in HP as:
\[ x_1 = \frac{1}{a - d}, \quad x_2 = \frac{1}{a}, \quad x_3 = \frac{1}{a + d} \]
where \( a \) is the middle term and \( d \) is the common difference.
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