If a ,b ,c are non -zero real numbers and if the system of equations (a-1) x=y+z,(b-1)y=z+x,(c-1) z=x+y has a non -trivial solution, then prove that ab+bc+ca =abc .

If a , b , c are non-zero real numbers and if the system of equations (a-1)x=y+z , (b-1)y=z+x , (c-1)z=x+y has a non-trivial solution, then prove that a b+b c+c a=a b c

If a , b , c are non-zero real numbers and if the system of equations (a-1)x=y=z (b-1)y=z+x (c-1)z=x+y has a non-trivial solution, then prove that a b+b c+c a=a b c

If a, b are non-zero real numbers and if the system of equations (a-1)x=y+z, (b-1)y=z+x, (c-1)z=x+y , has a non-trivial solution, then ab+bc+ca equals

If a,b,c are non - zero real numbers and if the equations : (a-1)x=y+z,(b-1)y=z+x,(c-1)z=x+y has a non - trivial solution, ab+bc+ca equals :

If a , b , c are non-zero real numbers and if the system of equations (a-1)x=y+z (b-1)y=z+x (c-1)z=x+y has a non-trivial solution, then ab+bc+ca equals to (A) abc (B) a^2 - b^2 + c^2 (C) a+b -c (D) None of these

If a,b,c are non-zero real numbers and if the system of equations (a-1)x=y+z(b-1)y=z+x(c-1)z=x+y has a non-trivial solution,then ab+bc+ca equals to (A) abc( B) a^(2)-b^(2)+c^(2)(C)a+b-c( D ) None of these

If a, b, c are non-zero real numbers and if the equations (a-1) x = y +z, (b-1) y = z + x , (c - 1) z = x + y have a non-trival solution, then ab+bc+ca=

If a,b and c are non-zero real numbers and if the equation (a-1)x=y+z,(b-1)y=z+x, (c-1)z=x+y has a non-trival solution then ab+bc+ca equals to

If a,b and c are non-zero real numbers and if the equation (a-1)x=y+z,(b-1)y=z+x, (c-1)z=x+y has a non-trival solution then ab+bc+ca equals to