Question

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find : y²

Answer 1

 y² = `[( sqrt5 + 2 )/( sqrt5 - 2 )]^2 = [ 5 + 4 + 4sqrt5 ]/[ 5 + 4 - 4sqrt5  ] = [ 9 + 4sqrt5 ]/[ 9 - 4sqrt5 ]`

= `[ 9 + 4sqrt5 ]/[ 9 - 4sqrt5 ] xx [ 9 + 4sqrt5 ]/[ 9 + 4sqrt5 ] = ( 9 + 4sqrt5)^2/[(9)^2 - (4sqrt5)^2] = [ 81 + 80 + 72sqrt5 ]/[ 81 - 80 ]`

= `161 + 72sqrt5`