Let `a ,b >0,` let `5a-b ,2a+b ,a+2b` be in A.P. and `(b+1)^2, a b+1,(a-1)^2` are in G.P., then the value of `(a^(-1)+b^(-1))` is _______.

Answer

6

Explanation

For the given A.P., we have
`2(2a+b)=(5a-b)+(a+2b)`
`rArrb=2a` (1)
Also for the given G.P., we have
`(ab+1)^(2)=(a-1)^(2)(b+1)^(2)` (2)
Putting b=2a from (1) and (2), we get `a=0,-2,` or `1/4`
But `agt0`, so `a=1/4` and b=2a=`1/2`
Hence, `(a^(-1)+b^(-1))=2+4=6`