if x=2+root 3, then the value of x+ (1/×) is. please answer
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if x=2+root 3, then the value of x+ (1/×) is. please answer
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[tex]Here, x = 2 + \sqrt{3} \\ \\ x + \frac{1}{x} = 2 + \sqrt{3} \: \: + \frac{1}{2 + \sqrt{3} } \\ \\ = \frac{ {(2 + \sqrt{3} \: ) }^{2} + 1 }{2 + \sqrt{3} } \\ \\ = \frac{4 + 4 \sqrt{3 } \: + 3+ 1 }{2 + \sqrt{3} } \\ \\ = \frac{8 + 4 \sqrt{3} }{2 + \sqrt{3} } \\ \\ = \frac{4(2 + \sqrt{3} \: )}{2 + \sqrt{3} } \\ \\ = 4[/tex]
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