No, it is not possible for a body to have a constant speed but variable velocity. In physics, speed and velocity have specific definitions and are distinct concepts.
Speed refers to the magnitude of the velocity vector, which is the rate at which an object covers distance. It is a scalar quantity and does not consider direction. If the speed of an object remains constant, it means that the object covers the same amount of distance per unit of time without changing its rate.
Velocity, on the other hand, is a vector quantity that includes both magnitude (speed) and direction. It specifies the rate at which an object changes its position in a particular direction. If the velocity of an object is variable, it means either the magnitude or direction or both are changing.
Therefore, if the speed is constant, it implies that the magnitude of the velocity remains unchanged. Consequently, for the velocity to be variable, either the magnitude (speed) or the direction or both must be changing over time.