Most Important Selected Qs for JEE AdvancedMathematicsSequences and Series
Let A₁, A₂ ; G₁, G₂ and H₁, H₂ be two AM's, GM's and HM's respectively between two positive real numbers a and b , then:
Options
- AA₁ H₂=a b
- BA₁ H₂=a^2 b^2
- CG₁ G₂=a b
- DA₂ H₁=a b
Correct answer
D. A₂ H₁=a b
Step-by-step solution
aligned & A₁= 2 a+b 3 ; A₂= a+2 b 3 & G₁=a^ 2 / 3 b^ 1 / 3 ; G₂=a^ 1 / 3 b^ 2 / 3 & H₁= 3 a b a+2 b ; H₂= 3 a b 2 a+b & A₁ H₂= 2 a+b 3 3 a b 2 a+b =a b & G₁ G₂=a b & A₂ H₁= a+2 b 3 3 a b a+2 b =a b & aligned