Solution
$$x-\frac{1}{x}=1$$
Squaring on both sides,
$$x^2+\frac{1}{x^2}-2=1$$
$$x^2+\frac{1}{x^2}=3$$
Squaring on both sides,
$$x^4+\frac{1}{x^4}+2=9$$
$$x^4+\frac{1}{x^4}=7$$
Squaring on both sides,
$$x^8+\frac{1}{x^8}+2=49$$
$$x^8+\frac{1}{x^8}=47$$
Hence, the correct answer is Option C
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