Question

if x is equal to (7 + 4 √3), then (X + 1 by x )is equal to​

Answer 1

$\star\:\:\:\bf\large\underline\blue{Question:-}$

• If $x=7+4\sqrt{3}$, find the value of $x+\frac{1}{x}$

$\star\:\:\:\bf\large\underline\blue{Solution:-}$

Given,

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

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

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

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

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

$= 7 - 4\sqrt{3}$

Therefore,

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

$\implies x + \frac{1}{x} = 14$

$\star\:\:\:\bf\large\underline\blue{Answer:-}$

• $x + \frac{1}{x} = 14$