`a/(x-a)+b/(x-b)=(2c)/(x-c)`

Find x in terms of a,b and c(a)/(x-a)+(b)/(x-b)+(c)/(x-c)=2(c)/(x-c)x!=a,x!=b,x!=c

(a^2/(x-a)+b^2/(x-b)+c^2/(x-c)+a+b+c)/(a/(x-a)+b/(x-b)+c/(x-c))

Find x in terms of a , b and c : (a)/(x - a) + (b)/(x - b) = (2 c)/(x - c) , x - a , b , c

Show that the equation A^(2)/(x-a)+B^(2)/(x-b)+C^(2)/(x-c)+...+H^(2)/(x-h)=k has no imaginary root,where A,B,C,...., Handa,b,c,........., handk in R

Show that the equation A^2/(x-a)+B^2/(x-b)+C^2/(x-c)+.....+H^2/(x-h)=k has no imaginary root, where A,B,C....H and a,b,c....,and Kin R.

Show that the equation A^2/(x-a)+B^2/(x-b)+C^2/(x-c)+.+H^2/(x-h)=x+1 where A,B,C ,……, a,b,c and i are real cannot have imaginary roots.

Statement-1: If a, b, c, A, B, C are real numbers such that a lt b lt c , then f(x) = (x-a)(x-b)(x-c) -A^(2)(x-a)-B^(2)(x-b)-C^(2)(x-c) has exactly one real root. Statement-2: If f(x) is a real polynomical and x_(1), x_(2) in R such that f(x_(1)) f(x_(2)) lt 0 , then f(x) has at least one real root between x_(1) and x_(2)

Statement-1: If a, b, c, A, B, C are real numbers such that a lt b lt c , then f(x) = (x-a)(x-b)(x-c) -A^(2)(x-a)-B^(2)(x-b)-C^(2)(x-c) has exactly one real root. Statement-2: If f(x) is a real polynomical and x_(1), x_(2) in R such that f(x_(1)) f(x_(2)) lt 0 , then f(x) has at least one real root between x_(1) and x_(2)

If the roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are equal, then a^(2)+b^(2)+c^(2) is equal to