`a`, `b` and `c` are distinct real numbers such that `a:(b+c)=b:(c+a)`

If a, b and c are distinct positive real numbers such that Delta_(1) = |(a,b,c),(b,c,a),(c,a,b)| and Delta_(2) = |(bc - a^2, ac -b^2, ab - c^2),(ac - b^2, ab - c^2, bc -a^2),(ab -c^2, bc - a^2, ac - b^2)| , then

If a,b,c are distinct real numbers such that a+(1)/(b)=b+(1)/(c )=c+(1)/(a) , then evaluate abc.

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 and c are distinct positive real numbers such that bc,ca,ab are in G.P,then b^(2)>(2a^(2)c^(2))/(a^(2)+c^(2))

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 a, b, c are three distinct positive real numbers such that (b+c)/(a)+(c+a)/(b)+(a+b)/( c )gt k, then the grealtest value of k, is

If a, b, c are three distinct positive real numbers such that (b+c)/(a)+(c+a)/(b)+(a+b)/( c )gt k, then the grealtest value of k, is

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.

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