Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that x=c y+b z, y=a z+c x and z=b x+a y . Then a^2+b^2+c^2+2 a b c is equal to

Step-by-step solution

The system of equations x-c y-b z=0, c x-y+a z=0 and b x+a y-z=0 have non-trivial solution if | array ccc 1 & -c & -b c & -1 & a b & a & -1 array |=0 1 (1-a^2 )+c(-c-a b)-b(c a+b)=0 a^2+b^2+c^2+2 a b c=1 .