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\boxed{\huge{\red{Explaination}}}

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\huge{\blue{\underline{Given:}}}

x  +   \frac{1}{x}  = 2 \\  {x}^{2}   +  1 = 2x \\  {x}^{2}  - 2x  +  1 = 0 \\  {x}^{2}   - x - x  + 1 = 0 \\ x(x - 1) - 1(x - 1) = 0 \\ x = 1 \\

\huge{\underline{To\:find:}}

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

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