For a, b > 0, let 5a – b, 2a + b, a + 2b be in A.P. and (b + 1)2, ab + 1, (a – 1)2 are in G.P. thencompute (a–1 + b–1).

Hello Student,

5a – b, 2a + b, a + 2b be in A.P.
2(2a + b) = 5a – b + a + 2b
=>b=2a

Also,
(b + 1)² , ab + 1, (a – 1)²
So ab + 1 = root{(b + 1)² * (a – 1)²} = (b + 1)(a – 1)

IF I use + sign i will get a, b <0 but a, b >0 in question
So use – sign in above we get a= ¼
so b = ½

Put this values in (a–1 + b–1)

you will get the ans

Thanks,

I hope you understood

Approved