Question

if a = 9-4root5, find a²+1/a²​

Answer 1

Step-by-step explanation:

a=9-4root5

1/a=1/9-4root5

1/a=1/9-4root5 × 9+4root5/9+4root5

1/a=9+4root5/9²-(4root5)²

1/a=9+4root5/81-80

1/a=9+4root5/1

1/a=9+4root5

a +1/a=9-4root5+9+4root5

a +1/a=18

(a+1/a)²=(18)²

a²+1/a²+2=324

a²+1/a²=324-2

a²+1/a²=322

Answer 2

Answer:

322

Step-by-step explanation:

(a+1/a)^2-2

(9-4√5+9+4√5)^2-2

322