If $5 x-\frac{1}{4 x}=6, x>0$, then find the value of $25 x^2-\frac{1}{16 x^2}$.

$6 \sqrt{41}$

If $5 x-\frac{1}{4 x}=6

then, If $5 x+\frac{1}{4 x}$ = ?

If x - \(\frac{1}{x}\)  = n

then 

If x + \(\frac{1}{x}\)  = \(\sqrt {n^2 + 4}\)

then, $5 x-\frac{1}{4 x}$ =  \(\sqrt {6^2 + 5}\)

$5 x-\frac{1}{4 x}$ =  \(\sqrt {6^2 + 5}\) =  \(\sqrt {41}\)

$25 x^2-\frac{1}{16 x^2}$ = ($5 x-\frac{1}{4 x}$) ($5 x-\frac{1}{4 x}$)

$25 x^2-\frac{1}{16 x^2}$ = (6)(\(\sqrt {41}\)) = $6 \sqrt{41}$