## Subject IV. (15 points)

Let $a_{k}=\sqrt{\left(k^{2}-k-2\right)\left(k^{2}+7 k+10\right)+36}, k \in \mathbb{N}^{*}$. Determine $n \in \mathbb{N}^{*}$ for which:

$\left[\sqrt{a_{1}}\right]+\left[\sqrt{a_{2}}\right]+\left[\sqrt{a_{3}}\right]+\cdots+\left[\sqrt{a_{n}}\right]=490$, where $[a]$ represents the integer part of the real number $a$.

Prof. Violin Gorcea, Avram Iancu Theoretical High School, Cluj-Napoca

## Grading Scale for 9th Grade (OLM 2015 - Local Stage)

## Official $10 p$

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