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

Question

If a, b, c and d are four positive real numbers such that a b c d=1 then minimum value of (1+a)(1+b)(1+c)(1+d) is (A) 4 (B) 1 (C) 16 (D) 18

Tardigrade Admin · Accepted Answer

1+ a ≥ 2 √ a 1+ b ≥ 2 √ b 1+ c ≥ 2 √ c 1+ d ≥ 2 √ d Now, (1+a)(1+b)(1+c)(1+d) ≥ 16 √a b c d (1+a)(1+b)(1+c)(1+d) ≥ 16.

Q. If $a, b, c$ and $d$ are four positive real numbers such that $ab c d = 1$ then minimum value of $(1 + a) (1 + b) (1 + c) (1 + d)$ is