If $x^{2}-3 x+1=0$, what is the value of $\left(x^{4}-\frac{1}{x^{4}}\right) ?$

x² – 3x + 1 = 0

$\Rightarrow x^{2}+1=3 x$

$\Rightarrow x+\frac{1}{x}=3$

On squaring both sides,

$x^{2}+\frac{1}{x^{2}}+2=9$

$\Rightarrow x^{2}+\frac{1}{x^{2}}=9-2=7$

On squaring again,

$x^{4}+\frac{1}{x^{4}}+2=49$

$\Rightarrow x^{4}+\frac{1}{x^{4}}=49-2=47$