### Instruction: If $(x + y)^2 = 1$ and $xy = -4$, what is the value of $x^2 + y^2$?### Response: To solve this problem, I will use the identity $(x + y)^2 = x^2 + 2xy + y^2$ and plug in the given values of $(x + y)^2$ and $xy$.
This gives me $1 = x^2 + 2(-4) + y^2$, which simplifies to $x^2 + y^2 = 9$.
Therefore, the value of $x^2 + y^2$ is 9.