Question

if x =9-4√5 then find x^2+1/x^2​

Answer 1

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GIVEN :-

x = 9 - 4√5

TO FIND :-

x²+1/x²

SOLUTION :-

x = 9 - 4√5

x² = 81 + 80 - 725

x² = 161 - 72√5

x² + 1/x² = 161-72√5 + 1/161-72√5

=> 161 - 72√5 + {161+72√5/(161)²-(72√5)²}

=> 161 - 72√5 + 161+72√5/25921-25920

=> 161 - 72√5 + 161 + 72√5

=> 322

So,

Required Value is 322.