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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. then compute (a–1 + b–1).

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. then
compute (a–1 + b–1).

Grade:11

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
6 years ago
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} = \pm (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

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