If $$\sqrt x = \sqrt 3 - \sqrt 5 {\text{,}}$$    then the value of x² - 16x + 6 is?

Solution (By Examveda Team)

$$\eqalign{ & \sqrt x = \sqrt 3 - \sqrt 5 \cr & \left( {{\text{Squaring both sides}}} \right) \cr & \Rightarrow x = 3 + 5 - 2.\sqrt {3.} \sqrt 5 \cr & \Rightarrow x = 8 - 2\sqrt {15} \cr & \Rightarrow x - 8 = - 2\sqrt {15} \cr & \left( {{\text{Squaring both sides}}} \right) \cr & \Rightarrow {x^2} + 64 - 16x = 60 \cr & \Rightarrow {x^2} + 4 - 16x = 0 \cr & \Rightarrow {x^2} + 6 - 16x = 2 \cr & \Rightarrow {x^2} - 16x + 6 = 2 \cr} $$