If x= p q-r , y= q r-p , z= r p-q , then (x y+y z+z x+1) is equal to

Step-by-step solution

aligned & x= p q-r y= q r-p z= r p-q & p-x q+x r=0....(i) & y p+q-y r=0....(ii) & z p-z q-r=0.....(iii) aligned This homogeneous system of equations in p, q, r can't have trivial solution, i.e. p q r 0 as it will make x, y, z not defined. Hence determinant of coefficients should be zero. aligned & i.e. | array ccc 1 & -x & x y & 1 & -y z & -z & -1 array |=0 & x y+y z+z x+1=0 aligned