a, b, c are reals such that a+b+c=3 and (1/a+b)+(1/b+c)+(1/c+a)=10/7 The value of (a/b+c) +(b/c+a)+(c/a+b) is________.

Let a ,b ,a n dc be distinct nonzero real numbers such that (1-a^3)/a=(1-b^3)/b=(1-c^3)/c dot The value of (a^3+b^3+c^3) is _____________.

Let a ,b and c be real numbers such that a+2b+c=4 . Find the maximum value of (a b+b c+c a)dot

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 and c represent the lengths of sides of a triangle then the possible integeral value of (a)/(b+c) + (b)/(c+a) + (c)/(a +b) is _____

If (1)/(a)+(1)/(c )=(1)/(2b-a)+(1)/(2b-c) , then

If a+c , a+b , b+c are in G.P and a,c,b are in H.P. where a , b , c gt 0 , then the value of (a+b)/(c ) 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 , b , c are positive numbers such that a gt b gt c and the equation (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 has a root in the interval (-1,0) , then

If a, b,c are three positive real numbers , then find minimum value of (a^(2)+1)/(b+c)+(b^(2)+1)/(c+a)+(c^(2)+1)/(a+b)

Let D_1=|a b a+b c d c+d a b a-b|a n dD_2=|a c a+c b d b+d a c a+b+c| then the value of |(D_1)/(D_2)|,w h e r eb!=0a n da d!=b c , is _____.