Let a, b be two positive numbers, where ab and 4( GM )=5( HM ) for the numbers, then a is equal to-

Question

Let a, b be two positive numbers, where a>b and 4( GM )=5( HM ) for the numbers, then a is equal to- (A) b (B) 2 b (C) 4 b (D) (1/4) b

Tardigrade Admin · Accepted Answer

4( GM )=5( HM ) ⇒ 4 √a b=5((2 a b/a+b)) ⇒ 4(a+b)2=25 a b ⇒ 4 a2-17 a b+4 b2=0 ⇒(4 a-b)(a-4 b)=0 ⇒ a=4 b (a=b / 4 neglecting)

Q. Let $a, b$ be two positive numbers, where $a > b$ and $4 (GM) = 5 (H M)$ for the numbers, then a is equal to-