Answers

2014-10-19T18:50:41+05:30
 x=9-4√5      [Given]
Taking reciprocal.

1/x=1/9-4√5
1/x = [1*(9+4√5)] / [(9-4√5)*(9+4√5)]
1/x=9+4√5/(81-80)
1/x=9+4√5

A.T.Q

x²+1/x²

(9-4√5)² + (9+4√5)²

[9²+(4√5)²-2×9×4√5]+[9²+(4√5)²+2×9×4√5)

[81+80-72√5]+[81+80+72√5]

161-72√5+161+72√5

=322

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