4. Determine $\overline{a b} \in N$ such that $\sqrt{a+\sqrt{\overline{a b}}}=a$

( Gheorghe Iacob, Paşcani problem E:14597 GM1/2014 )

## MATHEMATICAL OLYMPIAD - LOCAL STAGE 28.02.2015 - 7th GRADE SOLUTIONS AND ORIENTATIVE SCORING GUIDELINES

## Note: Each problem is scored from 0 to 7 points.

Any other solution is assimilated according to the scoring guidelines.
Subject 4.

| Details of solution | Associated mark |
| :--- | :---: | :---: |
| - demonstrates that $\overline{a b}$ is a perfect square....................................................................................................................................................................................... $3 \mathrm{p}$ |  |
| $-\quad$ determines $\overline{a b}=36 \ldots . . .$. |  |