If x, y, z ϵ R+ [ R+ denote real positive numbers] Then, aba+b is
Observe that aba+b is a part of HM of a & b i.e., HM = 2aba+b
Other relations in options are recognized as AM & GM.
As we know AM ≥ GM ≥ HM
(i) HM ≤ GM
⇒ 2aba+b ≤ (ab)12
⇒ aba+b ≤ (ab)122----------(1)
So, option C is true
(iii) HM ≤ AM
2aba+b ≤ a+b2
aba+b ≤ a+b4 --------------------------------(2)
So, option D is also true
From (1) & (2), right options are C, D