# If $\;x=\sqrt{2+\sqrt{2+\sqrt{2+------\;\infty}}}\;and\;y=\sqrt{2\;\sqrt{2\;\sqrt{2\;\sqrt{2\;----\;\infty}}}}$ then $xy$ equals

$(a)\;2\qquad(b)\;4\qquad(c)\;0\qquad(d)\;1$

Answer : (b) 4
Explanation : $x^2=x+2\quad\;x=2$
$y^2=2y\quad\;y=2$
$xy=4.$
answered Jan 20, 2014 by