SOLUTION: if a,b,c are in H.P then (1/a + 1/b - 1/c)(1/b + 1/c

SOLUTION: if a,b,c are in H.P then (1/a + 1/b - 1/c)(1/b + 1/c - 1/a)=?

Question 944201: if a,b,c are in H.P then (1/a + 1/b - 1/c)(1/b + 1/c - 1/a)=?
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!

Since a,b,c are in H.P., then 1/a,1/b,1/c are in A.P., so 1/b-1/a=1/c-1/b,
or 1/c = 2/b-1/a, substituting that for 1/c in

 (1/a + 1/b - 1/c)(1/b + 1/c - 1/a) 

ans simplifying, gives

((2b-a)(3a-2b))/(a^2b^2)

which is nothing special at all.

Edwin

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