50 is divided into 2 parts such that sum of their reciprocals is 1/12. Find the two parts ?

Question

50 is divided into 2 parts such that sum of their reciprocals  is  1/12. Find the two parts   ?

Answer

Analysis of the Problem:
Given that 50 is divided into two parts, let's assume the two parts are x and y. We need to find the values of x and y such that the sum of their reciprocals is 1/12.

Formulating the Equation:
The sum of the reciprocals of x and y can be represented as:
1/x + 1/y = 1/12
Solving this equation will give us the values of x and y.

Solving the Equation:
To solve the equation, we can first find a common denominator:
(1)(y) + (1)(x) = (1/12)(xy)
y + x = xy/12
Rearranging the equation, we get:
xy - 12x - 12y = 0
Using the quadratic formula, we can find the values of x and y:
x = [12 + sqrt(12^2 - 4(1)(-12))]/2(1) = [12 + sqrt(144 + 48)]/2 = [12 + sqrt(192)]/2
y = [12 - sqrt(192)]/2
Therefore, the two parts into which 50 is divided are:
x = [12 + sqrt(192)]/2
y = [12 - sqrt(192)]/2
Thus, x and y are the two parts into which 50 is divided such that the sum of their reciprocals is 1/12.

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