2. Solve in the set of integers the equation: $\sqrt{x^{2}-1900}=\left|\frac{x}{4}-4\right|-\sqrt{2017-x^{2}}$.

( Mathematical Gazette )
Subject 2: Solve in the set of integers the equation:

$$
\sqrt{x^{2}-1900}=\left|\frac{x}{4}-4\right|-\sqrt{2017-x^{2}}
$$

Author: Gazeta Matematica nr 11/ 2015

| Details of solution | Associated grading |
| :--- | :---: |
| $\sqrt{a}+\sqrt{b} \in Q ; a ; b \in \mathrm{N} \Rightarrow$ a, b perfect squares | $1 \mathrm{p}$ |
| $x^{2}-1900$ and $2017-x^{2}$ perfect squares | $1 \mathrm{p}$ |
| $1900 \leq x^{2} \leq 2017$ | $1 \mathrm{p}$ |
| $x^{2}=1936$ | $1 \mathrm{p}$ |
| $x \in\{-44 ; 44\}$ | $1 \mathrm{p}$ |
| $x=44$ does not verify | $1 \mathrm{p}$ |
| $x=-44$ unique solution | $1 \mathrm{p}$ |