If the 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)=`
A. -1
B. 1
C. 2
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, 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

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-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 equation a (y+z) = x, b (z+x) =y and c (x+y) = z, where a ne -1, be ne -1 , c ne - 1 , admit of non - trivial solutions , then : (1+a)^(-1) + (1+b)^(-1) +(1+c)^(-1) is

If the system of equations ax+y+z=0, x+by+z=0, x+y+cz=0 has a nontrivial solution. Where a!=1,b!=1,c!=1 , then a+b+c-abc=

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