[" 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)=]

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 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:

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 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