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  4. 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

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Q. 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

Sequences and Series

Solution:

$ 1+ a \geq 2 \sqrt{ a } $
$1+ b \geq 2 \sqrt{ b } $
$1+ c \geq 2 \sqrt{ c }$
$1+ d \geq 2 \sqrt{ d }$
Now, $(1+a)(1+b)(1+c)(1+d) \geq 16 \sqrt{a b c d}$
$(1+a)(1+b)(1+c)(1+d) \geq 16$.