Question 747021
{{{y=5/x}}}



{{{
x+5/x=5
}}}




{{{
x^2+5=5x
}}}



{{{
x^2-5x+5=0
}}}


this is clearly  irreducible...so let's use the quadratic formula...



{{{x = (-(-5) +- sqrt( (-5)^2-4*1*5 ))/(2*1) }}}



{{{x = (5 +- sqrt( 5 ))/2 }}}

So, yes if we extend our search out to all real numbers we can find two irrational numbers that meet our requirements


:)