Question

if a=2-√5/2+√5 and b=2+√5/2-√5.Find a²-b² ​

Answer 1

a²-b²
=[2-√5/2+√5]²-[2+√5/2-√5]²
=[2-√5]²/[2+√5]²-[2+√5]²/[2-√5]²
=[4+5-4√5/4+5+4√5]-[4+5+4√5/4+5-4√5]²
=[9-4√5/9+4√5]-[9+4√5/9-4√5]
=[9-4√5]²-[9+4√5]²/9²-[4√5]²
=81+80-72√5-81-80-72√5/81-80
=-144√5/1
=-144√5