Question

If a=9-4√5, Find the value of a 2 +1/a 2 .

Answer 1

(a+1/a)2=a2+1/a2+2
a2+1/a2=(a+1/a)2-2→ I
Now,
a=9-4root5
1/a=1/9-4root5
=(1/9-4root5)×9+4root5/9+4root5
=(9+4root5)
a+1/a=9-4root5+9+4root5
=81
Now,
a2+1/a2=(a+1/a)2-2 →(from I)
=(81)2-2
=6561-2
=6559