Question

if x = 2 + √3, then find the value of x + 1/x​

Answer 1

Given data,

$x = 2 + \sqrt{3}$

To calculate,

$x + \frac{1}{x} = ?$

Calculations,

$given \: that \\ x = 2 + \sqrt{3} \\ therefore \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3} \\ \frac{1}{x} = 2 - \sqrt{3} \\ hence \\ x + \frac{1}{x} = 2 + \sqrt{3} + 2 - \sqrt{3} \\ x + \frac{1}{x} = 4$

Final answer,

$x + \frac{1}{x} = 4$

(note that,

$(a + b)(a - b) = { a}^{2} - {b}^{2} \: \: )$

hope it helps to you☺️