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Diberikan bilangan real $p,q,r$ yang memenuhi $p+q+r=26$ dan $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=31$. Tentukan nilai dari  $\frac{p}{q}+\frac{q}{r}+\frac{r}{p}+\frac{p}{r}+\frac{r}{q}+\frac{q}{p}$.

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$p+q+r=26$, $\frac{1}{p}+\frac{1}{q}+\frac{1}{r}=31$.

\begin{align*}(p+q+r)\left(\frac{1}{p}+\frac{1}{q}+\frac{1}{r}\right)&=26\cdot 31\\1+\frac{p}{q}+\frac{p}{r}+\frac{q}{p}+1+\frac{q}{r}+\frac{r}{p}+\frac{r}{q}+1&=806\\\frac{p}{q}+\frac{q}{r}+\frac{r}{p}+\frac{p}{r}+\frac{r}{q}+\frac{q}{p}&=\boxed{803}.\end{align*}

 

 

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