if x=9-4root5 find value of x2+1/x2
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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
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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