If a2-2a-1=0, then find the value of aa+1/a2 . . .

Question : If a²-2a-1=0, then find the value of a²+1/a²?

Doubt by veer

Solution : 

a²-2a-1=0

dividing both sides by a
(a²-2a-1)/a=0/a
a²/a-2a/a-1/a=0/a
a-2-1/a=0
a-1/a=2 
S.B.S.
(a-1/a)²=(2)²
(a)²+(1/a)²-2(a)(1/a)=4 [∵(x-y)²=x²+y²-2xy]
a²+1/a²-2=4
a²+1/a²=4+2
a²+1/a²=6