Correct Answer: $\frac{58975}{20736}$

Solution : Given that: $x+\frac{1}{x}=\frac{25}{12}$
⇒ $12(x^2+1)=25x$
⇒ $12x^2-25x+12=0$
⇒ $12x^2-25x+12=0$
⇒ $12x^2-16x-9x+12=0$
⇒ $(4x-3)(3x-4)=0$
⇒ $x=\frac{4}3$ since $x>1$
$\therefore x^4-\left(\frac{1}{x}\right)^4$
Substituting the values,
$x^4-\left(\frac{1}{x}\right)^4= (\frac{4}3)^4-(\frac{3}4)^4$
$= \frac{256}{81}-\frac{81}{256}$
$= \frac{58975}{20736}$
Hence, the correct answer is $\frac{58975}{20736}$.