Question

if x=7-4root3, then the value of x-1/x is

Answer 1

Hello Mate!

$x = 7 - 4 \sqrt{3} \\ \frac{1}{ x} = \frac{1}{7 - 4 \sqrt{3} } \times \frac{7 + 4 \sqrt{3} }{7 + 4 \sqrt{3} } \\ = \frac{7 + 4 \sqrt{3} }{49 - (16 \times 3)} \\ = \frac{7 + 4 \sqrt{3} }{49 - 48} \\ = 7 + 4 \sqrt{3} \\ x + \frac{1}{x} = 7 - 4 \sqrt{ 3} - ( 7 + 4 \sqrt{3}) \\ = 7 - 4 \sqrt{3} - 7 - 4 \sqrt{3} \\ = - 8 \sqrt{3}$

Hope it helps☺!