Question

If $x=5-4\sqrt{6}$, find value of m:

$\frac{1}{x}$ $=-\frac{5+4\sqrt{6}}{m}$.

Answer 1

Given, $\frac{1}{x}=-\frac{5+4\sqrt{6}}{m}$............(1)

and $x=5-4\sqrt{6}$.

Then, $\frac{1}{x}=\frac{1}{5-4\sqrt{6}}$.

Rationalize the denominator,

$\frac{1}{x}=\frac{1}{5-4\sqrt{6}}\times \frac{5+4\sqrt{6}}{5+4\sqrt{6}}$

$=\frac{5+4\sqrt{6}}{25-16\times 6}$

$=-(\frac{5+4\sqrt{6}}{71})$..............(2)

Comparing (1) and (2), we get,

$m=71$.