Convergence of Sequences Given a Quadratic Sum Condition

Let $(u_n)$ and $(v_n)$ be two real sequences such that

$$ u_n^2+ u_n v_n + v_n^2 \xrightarrow[n\to+\infty] {}0.$$

Prove that the sequences $(u_n)$ and $(v_n)$ converge to 0.

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