If x² + y² + 1 = 2x, then the value of x³ + y⁵ is?

Solution (By Examveda Team)

$$\eqalign{ & {x^2} + {y^2} + 1 = 2x \cr & {x^2} - 2x + 1 + {y^2} = 0 \cr & {\left( {x - 1} \right)^2} + {y^2} = 0 \cr & {\text{If }}{{\text{A}}^2} + {{\text{B}}^2} = 0 \cr} $$
[As powers are even it can possible only when A = 0 & B = 0]
$$\eqalign{ & \therefore x - 1 = 0 \cr & x = 1 \cr & y = 0 \cr & \therefore {x^3} + {y^5} \cr & = 1 + 0 \cr & = 1 \cr} $$