Question

If x=2+root3 find the value of x+1\x

Answer 1

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

Answer 2

$hey \: freind \: here \: is \: your \: answer.$
x = 2 + √3
1 / x = 1 / 2 + √3
$now \: ratinalising \: the \: denomintor \:$
$multiplying \: 2 - \sqrt{3} \: to \: both \: numerator \: and \: denomntor$

1 / x = 1 / 2 + √3 * 2 - √3 / 2 - √3
$using \: {a}^{2} \: - {b}^{2} \: = \: ( \: a - b \: )( a \: + b \: )$
1 / x = 2 - √3 / 2² - √3²
1 / x = 2 - √3 / 4 - 3
1 / x = 2 - √3
$now \: finding \: x + 1 \div x$
x + 1 / x = 2 + √3 + 2 - √3
x + 1 / x = 4
$hope \: it \: helps$