A Nice Algebra Problem | Math Olympiad | A Nice Equation

[@subratabiswas2502]

4-√15= (4-√15)(4+√15)/(4+√15)=16-15/4+√15= 1/(4+√15) ; (4-√15)^x=1/(4+√15)^x ; Let (4+√15)^x= y ; so, y+1/y=62 ; i,e y^2+1=62y ; i,e y^2-62y+1=0 ; i,e y= [62+√62^2-4]/2 or y=[62-√62^2-4]/2 ; i,e y= [62+√3840]/2 or y=[62-√3840]/2 or x=(62+16√15)/2 or y=(62-16√15)/2 so, x=31+8√15 or x=31-8√15.