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 ,a n dc be distinct nonzero real numbers such that (1-a^3)/a=(1-b^3)/b=(1-c^3)/cdot The value of (a^3+b3+c^3) is _____________.

If a, b, c are positive real numbers, then the least value of (a+b+c)((1)/(a)+(1)/(b)+(1)/( c )) , is

a, b, c are reals such that a+b+c=3 and 1/(a+b) + 1/(b+c) + 1/ (c+a) = 10/3 . 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 _____________.

If a, b, c are positive real numbers such that a+b+c=1 , then the greatest value of (1-a)(1-b)(1-c), is

If the roots of the equation a(b-c)x^2+b(c-a)x+c(a-b)=0 are equal, show that 2//b=1//a+1// c dot

If the points A(-1,-4),B(b , c)a n dC(5,-1) are collinear and 2b+c=4, find the values of b and 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, a_1 ,a_2----a_(2n-1),b are in A.P and a,b_1,b_2-----b_(2n-1),b are in G.P and a,c_1,c_2----c_(2n-1),b are in H.P (which are non-zero and a,b are positive real numbers), then the roots of the equation a_nx^2-b_nx |c_n=0 are (a) real and unequal (b) real and equal (c) imaginary (d) none of these

Let a,b and c be the roots of x ^(3) -x+1 =0, then the ralue of ((1)/(a+1)+(1)/(b+1)+(1)/(c+1)) equals to :