If x2 + y2 + 2x +1 = 0, then the value of x31 + y35 is?

Answer: Option A

$$\begin{array}{rl}& x^2+y^2+2x+1=0\\ & \Rightarrow {\left(x+1\right)}^2+y^2=0\\ & \\ & \text{Let }{\left(x+1\right)}^2=0\\ & y^2=0\\ & x=-1,y=0\\ & \text{Now, }{x}^{31}+y^{35}\\ & ={\left(-1\right)}^{31}+{\left(0\right)}^{35}\\ & =-1\end{array}$$