Question

if x=root(7+4root3) then x=1/x

Answer 1

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

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

Rationalize the denominator,

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

$= (7 - 4 \sqrt{3} )( {7}^{2} - (4 \sqrt{3} ) {}^{2}$

$= (7 - 4 \sqrt{3} )(49 - 48)$

$\frac{1}{x} = 7 - 4 \sqrt{3} - - - (2)$

Therefore,

$x + \frac{1}{x} = (1) + (2)$

$= 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3}$

$= 14$

I hope this helps u :)