If $${y^4} + \frac{1}{{{y^4}}} = 223$$   and y > 1, then find the value of $${y^2} + \frac{1}{{{y^2}}}?$$

Solution (By Examveda Team)

$$\eqalign{ & {y^4} + \frac{1}{{{y^4}}} = 223 \cr & \Rightarrow {y^2} + \frac{1}{{{y^2}}} = \sqrt {223 + 2} \cr & \Rightarrow {y^2} + \frac{1}{{{y^2}}} = \sqrt {225} \cr & \Rightarrow {y^2} + \frac{1}{{{y^2}}} = 15 \cr} $$