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The sum of three numbers in H.P. is 24 and the sum of their reciprocals is 1/2.Then the numbers are ?

The sum of three numbers in H.P. is 24 and the sum of their reciprocals is 1/2.Then the numbers are ?

Grade:Upto college level

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Please find the answer to your question below
let the 3 numbers are 1/a-d,1/a,1/a+d
as sum of reciprocals is ½
3a=1/2 so a=1/6
and also given their sum is 24
so (6/1-6d)+(6)+(6/1+6d)=24
above eqquation on solving gives d=1/6\sqrt{3}
so the numbers are (\sqrt{3}-1/6\sqrt{3}),(1/6),(\sqrt{3}+1/6\sqrt{3})

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