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Algebra challenge

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anemone

MHB POTW Director
Staff member
Feb 14, 2012
3,802
Let $p,\,q,\,r,\,s,\,t \in \mathbb {R_+}$ satisfying

$p^2+pq+q^2=s^2\\ q^2+qr+r^2=t^2\\r^2+rp+p^2=s^2-st+t^2$

Prove that

$\dfrac{s^2-st+t^2}{s^2t^2}=\dfrac{r^2}{q^2t^2}+\dfrac{p^2}{q^2s^2}-\dfrac{pr}{q^2ts}$