If √$x+1/$√$x=3$, what is the value of $x+1/x$?

Square both sides. The left side expands to $(\surd x{)}^2+2\times$ √$x\times 1/$√$x+(1/\surd x{)}^2=x+2+1/x$, and the right side is 9. So $x+2+1/x=9$, giving $x+1/x=7$. The trap is 9: squaring term by term and forgetting the middle term 2 leaves $x+1/x=9$.