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If a,b,c and d are four positive real nu...

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

A

`4`

B

`1`

C

`16`

D

`18`

Text Solution

Verified by Experts

The correct Answer is:
C
If `a, b, c and d` …….
`1+a ge 2sqrt(a), 1+b ge 2sqrt(b), 1+c ge 2sqrt(c ), 1+d ge 2sqrt(d)`
`:. (1+a)(1+b)(1+c)(1+d)ge 16 sqrt(abcd) = 18`
`:.` minimum vslue of `(1+a) (1+b) (1+c) (1+d)` is `16`
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