Soln of non standard problem

xyz+z=a
xyz²+z=b
x²+y²+z²=4

Hint:(q2)
Replace x and y by -x and -y eqn remains unchanged

This is very tough.. will i have to study for IIT studies?

a=0?

Almost there....

if x=-x and y=-y lead to same eqn. then for unique soln. x=y=0 else if x=γ(say λ≠0) then x=-λ is also soln so x=0 similalrly y=0,
now z=z0 (say) put x=y=0 and z=z0 in original eqns now........

oopss.. last step me gadbad kar diye

so (a,b)=±2

so..... q.(1)'s ans is a=0 naa?? or sumthing else??