If `a=(2-sqrt(5))/(2+sqrt(5))` and `b=(2+sqrt(5))/(2-sqrt(5)),` find `a^2-b^2`

Explanation

`a²-b²`
`[(2+√5)/(2-√5)]^2 - [(2-√5)/(2+√5)] `
=`[(4+5+4√5)/( 4+5-4√5)] - [( 4+5-4√5) /(4+5+4√5)]`
`[9+4√5]/ [9-4√5 ]-[9-4√5]/[ 9+4√5]`
`[(9+4√5)² – (9−4√√5)²]/[(9-4√5) (9+4√√5)]`
`[(81+80+72√5) - (81+80-72√5)]/(81-80)`
= `144√5`.