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 ne three distinct non-zero real numbers satisfying the system of equation (1)/(a)+(1)/(a-1)+(1)/(a-2)=1 , (1)/(b)+(1)/(b-1)+(1)/(b-2)=1 , (1)/(c )+(1)/(c-1)+(1)/(c-2)=1 . Then abc=

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 in G.P. then prove that 1/(a^2-b^2)+1/(b^2)=1/(b^2-c^2)dot

Let a ,b ,a n dc be any three nonzero complex number. If |z|=1a n d' z ' satisfies the equation a z^2+b z+c=0, prove that a ( bara) =c (barc) a n d|a||b|=sqrt(a c( bar b )^2)

Find the value of a, b, c, d from the equation ((a-b,2a+c),(2a-b,3c+d))=((1,5),(0,2))

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

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

Let cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x)b epidot If x satisfies the equation a x^3+b x^2+c x-c_1=0, then the value of (b-a-c) is_________