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

Solution (By Examveda Team)

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