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## Answers

*x=9-4√5*

*1*

*=*

*1*

*x 9-4√5*

*Rationalising the equation*

*1*

*=*

*1*

*× 9+4√5*

*x 9-4√5*

*9+4√5*

*1*

*=*

*9+4√5*

*x 81-80*

*1*

*= 9+4√5*

*x*

*x²=(9-4√5)² = 81+80 - 72√5*

*1*

*= (9+4√5)²= 81+80+72√5*

*x²*

*x²+1/x² = 161-72√5+161+72√5*

*x²+1/x² = 161+161*

*x²+1/x²=322*### This Is a Certified Answer

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So given x = 9 - 4√5

1/x = 1/(9 - 4√5)

= 9 + 4√5 after rationalizing

so we know (a+b)² + (a-b)² = 2(a² + b²)

so substituting the values

= 2(81 + 80)

= 2 x 161 = 322

1/x = 1/(9 - 4√5)

= 9 + 4√5 after rationalizing

so we know (a+b)² + (a-b)² = 2(a² + b²)

so substituting the values

= 2(81 + 80)

= 2 x 161 = 322

__ANSWER__