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If 1/(b-a)+1/(b-c)=1/a+1/c,then a,b,c are in ....... A)AP. B)GP C)HP. D)in GP and HP both

If 1/(b-a)+1/(b-c)=1/a+1/c,then a,b,c are in .......
A)AP.           B)GP
C)HP.           D)in GP and HP both

Grade:12th pass

1 Answers

vinit arora
15 Points
3 years ago
Ans is c hp see put the value of b =2ac/a+c in rhs you will get 1/a +1/b  see how
=1/2ac-a(a+c)/ac + 1/2ac-c(a+c)/ac
=a+c/a(c-a) -  a+c/c(c-a)
=a+c/ac
=1/a + 1/c
Hence proved that a, b, c are in hp

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