Question

If a, b, c and d are four positive real numbers such that abcd = 1, the minimum value of (1 + a) (1 + b) (1 + c) (1 + d) is

• A. 4
• B. 1
• C. 16
• D. 18

Answer 1

Answer: (C)

16

Answer 2

1 + a ³ $2 \sqrt { \mathrm { a } }$ {A.M. ³ G.M.}

1 + b ³

1 + c ³

1 + d ³ $2 \sqrt { \mathrm { d } }$

\1 + a) (1 + b) (1 + c) (1 + d) ³ 16= 16

\min. value = 16 (for a = b = c = d = 1)