If `a , b , c ,` are positive real numbers, then prove that (2004, 4M) `{(1+a)(1+b)(1+c)}^7>7^7a^4b^4c^4`

If a,b,c, are positive real numbers,then prove that (2004,4M){(1+a)(1+b)(1+c)}^(7)>7^(7)a^(4)b^(4)c^(4)

If a,b,c are positive real no., then prove that [(1+a)(1+b)(1+c)]^7 gt 7^7a^4b^4c^4 .

If a,b,c are positive unequal real numbers then prove that (a+b+c)(1/a+1/b+1/c)gt9

If a,b,c are positive real numbers then (1+a)^7(1+b)^7(1+c)^7 (A) lt7^7a^4b^4c^4 (B) le7^7a^4b^4c^4 (C) gt7^7a^4b^4c^4 (D) none of these

If a, b, c and d are positive real numbers such that a+b+c+d= 1 then prove that ab + bc + cd + da le 1/4 .

If a, b, c are distinct positive real numbers such that a+(1)/(b)=4,b+(1)/( c )=1,c+(1)/(d)=4 and d+(1)/(a)=1 , then

If a, b, c are distinct positive real numbers such that a+(1)/(b)=4,b+(1)/( c )=1,c+(1)/(d)=4 and d+(1)/(a)=1 , then

If a,b,c,d are four positive real numbers such that abcd=1 then least value of (a+4)(b+4)(c+4)(d+4) is

If a,b,c,d are four positive real numbers such that abcd =1 then find the least value of (a+4) ( b+4) ( c+4) (d+4) .

If a ,b ,c are non-zero real numbers, then the minimum value of the expression (((a^4+ 3a^2+1)(b^4+5b^2+1)(c^4+7c^2+1))/(a^2b^2c^2)) is not divisible by prime number.