\(x + \frac{1}{x} = \sqrt 5 \) হলে, \(x3 + \frac{1}{{x3}}\) = এর মান কত ?  

A  \(2\sqrt 5 \) 

B \(3\sqrt 5 \) 

C \(4\sqrt 5 \) 

D \(5\sqrt 5 \) 

Solution

Correct Answer: Option A

 দেওয়া আছে,  \(x + \frac{1}{x} = \sqrt 5 \)  

  \(x3 + \frac{1}{{x3}} = (x + \frac{1}{x})3 - 3.x.\frac{1}{x}(x + \frac{1}{x})\)  ( 

  = \((\sqrt 5 )3 - 3\sqrt 5 \)  

  = \(\sqrt {5.(} \sqrt 5 )2 - 3\sqrt 5 \) 

 = \(5\sqrt 5  - 3\sqrt 5 \)  (5টি  \(\sqrt 5 \) থেকে 3টি  \(\sqrt 5 \) বিয়োগ করতে হবে )  = \(2\sqrt 5 \)  

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