Question

the A.M,G.M, and H.M between two positive numbers a and b are equal than

Answer 1

So AM = (a+b)/2 ; GM =√(ab) ; HM = 2ab/(a+b)

AM=HM ⇒ (a+b) ² = 4ab

⇒ a² +2ab + b² = 4ab

⇒ a² -2ab + b² = 0

⇒(a-b)² = 0

⇒ a=b

So GM =√(ab) = a which is also equal to AM