Home
Class 12
MATHS
If the system of linear equations a(y + ...

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`

Promotional Banner

Similar Questions

Explore conceptually related problems

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 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!=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

Prove that the system of equations in xa +y+z=0 , x +by +z=0 , x +y+cz=0 has a non - trivial solution 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 equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero solution, then the possible value of k are -1,2 b. 1,2 c. 0,1 d. -1,1

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

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