Question 1067585
{{{highlight_green(x^2+(1/x)^2-(x+1/x)=7/4)}}}



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{{{x^2+1/x^2-x-1/x=7/4}}}, best common denominator is {{{4x^2}}}.


{{{4x^2*x^2+4x^2(1/x^2)-4x^2*x-4x^2(1/x)=4x^2(7/4)}}}


{{{4x^4+4-4x^3-4x=7x^2}}}


{{{4x^4-4x^3-7x^2-4x+4=0}}}
You can try checking possible roots of PLUS&MINUS of 1/4, 1/2, 1, 2, 4 according to Rational Roots Theorem and synthetic division.  The only two REAL (and rational) roots found will be  {{{1/2}}} and {{{2}}}.


{{{system(x=2,and,1/x=1/2)}}}
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