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Let \small x=(9+4 \sqrt{5})^{19} , then x{x} ({⋅} denotes fractional part of x) is equal to 
 

Option: 1

2^{19}


Option: 2

3^{19}


Option: 3

1


Option: 4

None of these


Answers (1)

best_answer

\begin{aligned} & x=(9+4 \sqrt{5})^{19}=[x]+\{x\} \\ & \{x\}+(9-4 \sqrt{5})^{19}=1 \\ & x\{x\}+1=x \\ & x\{x\}=(9+4 \sqrt{5})^{19}-1 \end{aligned}

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chirag

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