Question

if x= 3+2root3 find the value of (x-1/x)

Answer 1

(3+2√3)^2-1/3+2√3=9+12+12√3-1/3+2√3
=20+12√3/3+2√3 ×3-2√3/3-2√3
=60-40√3+36√3-72/-3=-12-4√3/-3
=-4(3+√3)/-3=4(3+√3)/3
is your answer

Answer 2

Solution:-

given:-

$x = 3 + 2 \sqrt{3} \\ x - \frac{1}{x} \\ 3 + 2 \sqrt{3} + \frac{1}{3 + 2 \sqrt{3} } \\ \frac{9 + 12 + 12 \sqrt{3} }{3 + 2 \sqrt{3} } \times \frac{3 - 2 \sqrt{3} }{3 - 2 \sqrt{3} } \\ \frac{63 + 36 \sqrt{3} - 42 \sqrt{3} - 72 }{9 - 12} \\ \frac{ - 6 \sqrt{3} - 9}{ - 3} \\ \frac{ - 3(3 + 2 \sqrt{3}) }{ - 3} \\ (3 + 2 \sqrt{3} ) \: ans$