If a,b, and c are distinct positive real number such that `a+b+c=1`, then prove that `((1+a)(1+b)(1+c))/((1-a)(1-b)(1-c))gt8` .

If a ,b , a n dc are distinct positive real numbers such that a+b+c=1, then prove tha ((1+a)(1+b)(1+c))/((1-a)(1-b)(1-c))> 8.

If a , b ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3a cdot

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 distinct +ve real numbers and a^(2)+b^(2)+c^(2)=1" then "ab+bc+ca is

If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , then prove that either x >3.

If a ,b ,c are three distinct real numbers in G.P. and a+b+c=x b , then prove that either x >3.

If a,b,c are real numbers such that 0 lt a lt 1, 0 lt b lt 1, 0 lt c lt 1, a + b + c = 2 , then prove that (a)/(1 - a) (b)/(1 - b) (c )/(1 - c) ge 8 .

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 ,b ,c are distinct positive numbers, then the nature of roots of the equation 1//(x-a)+1//(x-b)+1//(x-c)=1//x is Option a) all real and is distinct Option b) all real and at least two are distinct Option c) at least two real Option d) all non-real

If a+b+c=1, then prove that 8/(27a b c)>{1/a-1}{1/b-1}{1/c-1}> 8.