[tex]x+\frac{1}{x}=4 |()^2\\
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x^2+2\cdot x\cdot \frac{1}{x}+\frac{1}{x^2}=16\\
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x^2+\frac{1}{x^2}+2=16\\
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x^2+\frac{1}{x^2}=14\ |()^2\\
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x^4+2\cdot x^2\cdot \frac{1}{x^2}+\frac{1}{x^4}=196\\
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x^4+\frac{1}{x^4}+2=196\\
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\boxed{x^4+\frac{1}{x^4}=194}[/tex]