Soln of non standard problem

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?

i guess x=0 and y=1 ...
will give the solution..

i think on that point.. dont ask why!

a=0?

question 2 is simple after hint...

(x,y,z) is solution then (-x,-y,z) is another solution.

so for unique..

x=-x
y=-y

so x=0=y

so z=±2

so (a,b)=±4

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........