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)`.

Explanation

`therefore a,b,c " are in AP."`
Let `a=A-D, b=A, c=A+D`
Then, `a=b-D, c=b+D`
Now, `abc=4`
`(b-D)b(b+D)=4`
`implies b(b^(2)-D^(2))=4`
`implies b^(2)-D^(2)ltb^(2)`
`implies b(b^(2)-D^(2)) lt b^(3) implies 4ltb^(3)`
`therefore " " bgt (4)^((1)/(3))" or " bgt (2)^((2)/(3))`
Hence, the minimum value of b is `(2)^((2)/(3))`