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

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

If a+1/b = 1 and b+1/c=1 then prove that c+1/a =1

Prove that (a^8+b^8+c^8)/(a^3b^3c^3)>1/a+1/b+1/c

Prove that (a^8+b^8+c^8)/(a^3b^3c^3)>1/a+1/b+1/c

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

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

If a ,b ,c in R+ form an A.P., then prove that a+1//(b c),b+1//(1//a c),c+1//(a b) are also in A.P.

If a,b, and c 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 b is the harmonic mean between a and c, then prove that (1)/(b - a) + (1)/(b - c) = (1)/(b) + (1)/(c)