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 _____________.

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 ,c are three distinct positive real numbers in G.P., then prove that c^2+2a b >3a cdot

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 , in R such that a+b=1a n d(1-2a b)(a ^3+b^3)=12 . The value of (a^2+b^2) is equal to____.

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 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

Let z_1, z_2, z_3 be the three nonzero complex numbers such that z_2!=1,a=|z_1|,b=|z_2|a n d c=|z_3|dot Let |(a, b, c), (b, c, a), (c,a,b) |=0 a r g(z_3)/(z_2) equal to (a) arg((z_3-z_1)/(z_2-z_1))^2 (b) orthocentre of triangle formed by z_1, z_2, z_3, i sz_1+z_2+z_3 (c)if triangle formed by z_1, z_2, z_3 is equilateral, then its area is (3sqrt(3))/2|z_1|^2 (d) if triangle formed by z_1, z_2, z_3 is equilateral, then z_1+z_2+z_3=0