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 (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,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 are positive real numbers and 2a+b+3c=1 , then the maximum value of a^(4)b^(2)c^(2) is equal to

If a and b are positive real numbers such that a+b =c, then the minimum value of ((4 )/(a)+ (1)/(b)) is equal to :

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^(2)b^(2)c^(2))) is not divisible by prime number.

If a,b,c are non-zero real numbers, then the minimum value of the expression ((a^(8)+4a^(4)+1)(b^(4)+3b^(2)+1)(c^(2)+2c+2))/(a^(4)b^(2)) equals

If 27 abc> (a+b+c)^3 and 3a +4b +5c=12 then 1/a^2+1/b^3+1/c^5=10, where a, b, c are positive real numbers. Statement-2: For positive real numbers A.M.>= G.M.