Question
If arithmetic mean of two distinct positive real number a and b(a b) be twice their geometric mean, then a: b=
BITSAT
Mathematics
Sequences and Series
2024
BITSAT 2024 (Memory Based Paper 1)
BITSAT Mathematics Question (2024) — Solution
Options
- A. (2+ 3 ):(2- 3 )
- B. (2+ 5 ):(2- 5 )
- C. (2+ 2 ):(2- 2 )
- D. None of these
Answer
A. (2+ 3 ):(2- 3 )
Step-by-step solution
By the given condition, a+b 2 =2 a b a+b=4 a b Now, (a-b)^2=(a+b)^2-4 a b=16 a b-4 a b= 12 a b a-b= 12 a b =2 3 a b . (Taking + ve sign only as a b) a+b a-b = 4 a b 2 3 a b = 2 3 By componendo and dividendo, 2 a 2 b = 2+ 3 2- 3 or a b = 2+ 3 2- 3
Related: Mathematics — Sequences and Series · All PYQ Banks