Divide 27 into two two parts such that sum of their reciprocal is 3 by 20
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let the nos. be x and y
x + y = 27 ---- (1)
1/x + 1/y = 3/20
(x + y)/xy = 3/20
put x + y = 27
27 / xy = 3/20
xy = 180
x = 180/y
putting in (1)
180 + y² - 27 y = 0
solve the equation to get y = 15 or 12
and then x = 12 or 15
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