If the system of equation `x= a(y +z),y =b(z +x),z =c (x + y), (a,b,c !=-1)` has a non-zero solution then the value of `a/(a+1)+b/(b+1)+c/(c+1)` is

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:

If the system of equation ax+y+z=0, x+by+z=0, x+y+cz=0,(a,b,c!=1) has non trivial solution (non -zero solution) then 1/(1-a)+1/(1-b)+1/(1-c)=

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 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 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 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