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 _____________.

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________.

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

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

Let a , b ,a n dc be rel numbers which satisfy the equation a+1/(b c)=1/5,b+1/(a c)=(-1)/(15),a n dc+1/(a b)=1/3dot The value of (c-b)/(c-a) is equal to ________.

Let a , b , c , d be positive integers such that (log)_a b=3/2a n d(log)_c d=5/4dot If (a-c)=9, then find the value of (b-d)dot

Let a,b,c,d be real numbers such that |a-b|=2, |b-c|=3, |c-d|=4 Then the sum of all possible values of |a-d|=

If z_1, z_2, z_3 are distinct nonzero complex numbers and a ,b , c in R^+ such that a/(|z_1-z_2|)=b/(|z_2-z_3|)=c/(|z_3-z_1|) Then find the value of (a^2)/(z_1-z_2)+(b^2)/(z_2-z_3)+(c^2)/(z_3-z_1)

If a x^2+b x+c=0a n db x^2+c x+a=0 have a common root and a, b, and c are nonzero real numbers, then find the value of (a^3+b^3+c^3)//a b c

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