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If 1/(b-a)+1/(b-c)=1/a+1/c , then (A). a...

If `1/(b-a)+1/(b-c)=1/a+1/c ,` then (A). `a ,b ,a n dc` are in H.P. (B). `a ,b ,a n dc` are in A.P. (C). `b=a+c` (D). `3a=b+c`

A

a,b, and c are in H.P

B

a,b, and c are in A.P

C

b=a+c

D

3a= b+c

Text Solution

Verified by Experts

The correct Answer is:
A, B
`1/(b-a)+1/(b-c)=1/a+1/c`
or `1/(b-a)-1/c=1/a-1/(b-c)`
or `(c-b+a)/(c(b-a))=(b-c-a)/(a(b-c))`
`rArrc-b+a=0` or `1/(c(b-a))=1/(a(c-b))`
`rArrb=a+c` or bc-ac=ac-ab
`rArrb=a+c`or `b=(2ac)/(a+c)`
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