$$\sqrt {2 + \sqrt {2 + \sqrt {2 + ......} } } $$      is equal to ?

$$\eqalign{ & x = \sqrt {2 + \sqrt {2 + \sqrt {2 + ......} } } \cr & \Rightarrow {x^2} = 2 + \sqrt {2 + \sqrt {2 + .......} } \cr & \Rightarrow {x^2} = 2 + x \cr & \Rightarrow {x^2} - x - 2 = 0 \cr & \Rightarrow x\left( {x - 2} \right) + 1\left( {x - 2} \right) = 0 \cr & \Rightarrow \left( {x + 1} \right)\left( {x - 2} \right) = 0 \cr & \Rightarrow x = 2 \cr} $$