Question

if x=7+√3 find the value of x+1/x

Answer 1

the value of x is given
therefore, 1/x = 7-√3 (by rationalising)
now,
x +1/x
(7+√3) + (7-√3)
7^2 + √3^2
49 +3
52

Answer 2

Hey mate !

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Given :

$x = 7 + \sqrt{3}$

$\frac{1}{x} = \frac{1}{7 + \sqrt{3} } \times \frac{7 - \sqrt{3} }{7 - \sqrt{3} } \\ \\ \\ \frac{1}{x} = \frac{7 - \sqrt{3} }{(7) {}^{2} - ( \sqrt{3}) {}^{2} } \\ \\ \frac{1}{x} = \frac{7 - \sqrt{3} }{49 - 3} \\ \\ \frac{1}{x} = \frac{7 - 4 \sqrt{3} }{46}$

Now,

$x + \frac{1}{x} \\ \\ 7 + \sqrt{3} + \frac{7 - \sqrt{3} }{46} \\ \\ \frac{46(7 + \sqrt{3}) + 7 - \sqrt{3} }{46} \\ \\ \frac{322 + 46 \sqrt{3} + 7 - \sqrt{3} }{46} \\ \\ \frac{329 + 45 \sqrt{3} }{46}$


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Thanks for the question !

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