Question

If a=2+root 3/2-root 5 and b=2- root 5/ 2+ root 5 then find the value of a square - b square

Answer 1

a=2+√3/2-√5
a^2=4+4√3+3/4-4√5+5
=7+4√3/9-4√5
b=2-√5/2+√5
b^2=4-4√5+5/4+4√5+5
=9-4√5/9+4√5
a^2-b^2=(7+4√3)(9+4√5)-(9-4√5)^2/81-80
=63+28√5+36√3+16√15-(81-72√5+80)/1
=63+28√5+36√3+16√15-81+72√5-80
=-98+100√5+36√3+16√15