Question

find the value of x-1/x if value of x is 7+4√3​

Answer 1

$x = 7 + 4 \sqrt{3} \\ = > \frac{1}{x} = \frac{1}{7 + 4 \sqrt{3} } \\ = > \frac{1}{x} = \frac{1(7 - 4 \sqrt{3}) }{(7 + 4 \sqrt{3})( 7 - 4 \sqrt{3} )} \\ = > \frac{1}{x} = \frac{7 - 4 \sqrt{3} }{ {(7)}^{2} - {(4 \sqrt{3)} }^{2} } \\ = > \frac{1}{x} = \frac{7 - 4 \sqrt{3} }{49 - 48} \\ = > \frac{1}{x} = \frac{7 - 4 \sqrt{3} }{1} \\ = > \frac{1}{x} = 7 - 4 \sqrt{3}$

Therefore,

$x - \frac{1}{x} \\ = 7 + 4 \sqrt{3} - (7 - 4 \sqrt{3)} \\ = 7 + 4 \sqrt{3} - 7 + 4 \sqrt{3} \\ = 8 \sqrt{3}$