Question 1133481
<pre>
The easiest way is just to solve {{{x+1/x=2}}} for x
and substitute in {{{x^4+1/x^4}}}

{{{x+1/x=2}}}

Multiply through by x

{{{x^2+x/x=2x}}}

{{{x^2+1=2x}}}

{{{x^2-2x+1=0}}}

{{{(x-1)(x-1)=0}}}

{{{x-1=0}}}

{{{x=1}}}

Substitute in 

{{{x^4+1^""/x^4}}}

{{{1+1^""/1}}}

{{{1+1}}}

{{{2}}}

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But maybe you meant "without solving for x". If so, then:

{{{x+1/x=2}}}

Square both sides:

{{{(x+1/x)^2=2^2}}}

{{{x^2+2(x)(1/x^"")+1/x^2=4}}}

{{{x^2+2+1/x^2=4}}}

{{{x^2+1/x^2=2}}}

Square both sides:

{{{(x^2+1/x^2)^2=2^2}}}

{{{x^4+2(x^2)(1/x^2)+1/x^4=4}}}

{{{x^4+2+1/x^4=4}}}

{{{x^4+1/x^4=2}}}

That was done without solving for x.

Edwin</pre>