New Year Challenge

anemone

MHB POTW Director
Staff member
Find all triples $(a,\,b,\,c)$ of real numbers such that the following system holds:

$a+b+c=\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\\a^2+b^2+c^2=\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}$