Dec 31, 2020 Thread starter Admin #1 anemone MHB POTW Director Staff member Feb 14, 2012 3,812 Find all triples $(a,\,b,\,c)$ of real numbers such that the following system holds: $a+b+c=\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\\a^2+b^2+c^2=\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}$

Find all triples $(a,\,b,\,c)$ of real numbers such that the following system holds: $a+b+c=\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\\a^2+b^2+c^2=\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{c^2}$