Divide 40 into 2 parts such that sum of their reciprocals is 8/75
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Define x :
Let one part = x
The other part = 40 - x
Solve x :
The sum of their reciprocals is 8/75
1/x + 1/(40 - x) = 8/75
(40 - x + x)/x(40 - x) = 8/75
40/x(40 - x) = 8/75
40(75) = 8x(40 - x)
3000 = 320x - 8x²
8x² - 320x + 3000 = 0
x² - 40x + 375 = 0
(x - 15) (x - 25) = 0
x = 15 or x = 25
Answer: The two parts are 15 and 25
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