2. Solve in $\mathrm{N}$ the equation $\left[\sqrt{n^{2}+4 n+9}\right]=3 n-4$, where $[x]$ represents the integer part of $x$.

B.M.
Solution: We have $\sqrt{(n+2)^{2}}0, \quad$ so $\quad\left[\sqrt{n^{2}+4 n+9}\right]=n+2 \quad$ for $\quad n>0$. $(4 p)$

The equation becomes $n+2=3n-4$, with the solution $n=3$.

For $n=0$ it does not verify.