Question

If x=1/7-4√3find x+1/x

Answer 1

Given,

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

then,

• $x + \frac{1}{x}$

• $\frac{1}{7 - 4\sqrt{3} } + \frac{1}{ \frac{1}{7 - 4\sqrt{3} } }$

• $\frac{1}{7 - {4 \sqrt{3} } } + 7 - 4 \sqrt{3}$

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

• $\frac{1 + 49 - 28 \sqrt{3} - 28 \sqrt{3} + 48 }{7 - 4 \sqrt{3} }$

• $\frac{98 - 97}{7 - 4 \sqrt{3} }$

• $\frac{1}{7 - 4 \sqrt{3} }$

is the required answer.