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 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 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 system of equations (a-1)x=y+z, (b-1)y=z+x and (c-1)z=x+y have a non - trivial solutin, then (3)/(2a)+(3)/(2b)+(3)/(2c) is equal to

If the system of equations x=c y+b z ,\ \ y=a z+c x ,\ \ z=b x+a y has a non-trivial solution show that a^2+b^2+c^2+2a b c=1

If a,b,c are distinct real numbers and the system of equations ax+a^(2)y+(a^(3)+1)z=0bx+b^(2)y+(b^(3)+1)z=0cx+c^(2)y+(c^(3)+1)=0 has a non-trivial solution,show that abc=-1

If a!=b!=c!=1 and the system of equations ax+y+z=0,x+by+z=0 ,x+y+cz=0 have non trivial solutions then a+b+c-abc

if the system of equation ax+y+z=0,x+by=z=0, and x+y+cz=0(a,b,c!=1) has a nontrival solution,then the value of (1)/(1-a)+(1)/(1-b)+(1)/(1-c)is: