Ifthe equations `a(y +z) =x,b(z+x) = y, c (x + y) = z` have nontrivial solutions, then `1/(1+a)+1/(1+b)+1/(1+c)=`

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=

a ,b ,c are distinct real numbers not equal to one. If a x+y+z=0,x+b y+z=0, and x+y+c z=0 have nontrivial solution, then the value of 1/(1-a)+1/(1-b)+(1)/(1-c) is equal to a. 1 b. -1 c. z e ro d. none of these

a ,b ,c are distinct real numbers not equal to one. If a x+y+z=0,x+b y+z=0,a n dx+y+c z=0 have nontrivial solution, then the value of 1/(1-a)+1/(1-b)+(1)/(1-c) is equal to a. 1 b. -1 c. z e ro d. none of these

If the system of linear equations a(y+z)-x=0,b(z+x)-y=0,c(x+y)-z=0 has a non trivial solution,(a!=-1,b!=-1,c!=-1), then show that (1)/(1+a)+(1)/(1+b)+(1)/(1+c)=2

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 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