# Interesting condition on three real numbers

Algebra Level pending

Choose the option which truthfully completes the following statement.

Let $$a,b,c \in \mathbb{R}$$ such that $$|a|, |b|, |c| \neq 1$$. Then $$\exists p,q,r \neq 0$$ such that $$a = \dfrac{q-r}{p}, b = \dfrac{r-p}{q}, c = \dfrac{p - q}{r}$$ if and only if...

$$A : a^3 + b^3 + c^3 = 3abc$$

$$B : ab + bc + ca = abc$$

$$C : a + b + c = -abc$$

$$D : ab + bc + ca = 0$$

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