The exercise asks to decompose $V(X^2+Y^2 -1, X^2 - Z^2 - 1) \subset \mathbb A^3(\mathbb C)$ into irreducible components.
I noticed that both polynomials are irreducible, but this didn’t help me really. I tried to find what the ideal $(X^2 +Y^2 -1, X^2 - Z^2 - 1)$ is, but I couldn’t find a reasonable alternative form (generators). Finally, I tried to write the set itself as the union of the four obvious subsets of $\mathbb A^3(\mathbb C)$ corresponding to the zeros of the above polynomials, but I am not sure if these are irreducible or how to decompose them into irreducible components.
This exercise is in the section corresponding to the Nullstellensatz.