Question
If a 0, b 0, c 0 and a, b, c are distinct, then (a+b)(b+c)(c+a) is greater than
BITSAT
Mathematics
Sequences and Series
2024
BITSAT 2024 (Memory Based Paper 3)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 2(a+b+c)
- B. 3(a+b+c)
- C. 6 a b c
- D. 8 a b c
Answer
D. 8 a b c
Step-by-step solution
We know that AM GM ...(i) Now, applying Eq. (i) in a and b a+b 2 a b ....(ii) applying Eq. (i) in b and c b+c 2 b c ....(iii) and applying Eq. (i) in c and a c+a 2 c a ....(iv) By E'qs. (ii), (iii) and (iv) array cc & (a+b)(b+c)(c+a) 8 a b c \\ & (a+b)(b+c)(c+a) 8 a b c array
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