Our Saviour would neither discourage the weak faith of this nobleman, nor yet encourage his weakness: he healeth his son for the encouragement of his faith; he doth it by his word, without going down to him, that he might not gratify his weakness, thinking his personal presence was necessary; he bids him go, for his son was recovered (that is here meant by liveth). Upon this his faith groweth, and he who before only believed Christ to be a prophet, probably upon others hearsay, now believeth his word, that is, was persuaded that his son was indeed recovered.
Related Commentaries of John 4:50
John 4:50
50 Jesus saith unto him,Go thy way; thy son liveth. And the man believed the word that Jesus had spoken unto him, and he went his way.