Subject 2. Find the real numbers $\mathrm{x}$ and $\mathrm{y}$ for which we have

$$
\sqrt{4 x^{2}-12 x+25}+\sqrt{4 x^{2}+12 x y+9 y^{2}+64} \leq 12
$$
## Subject 2.

|  | $\sqrt{4 x^{2}-12 x+25}=\sqrt{(2 x-3)^{2}+16} \geq 4$ | 2p |
| :--- | :--- | :---: |
|  | $\sqrt{4 x^{2}+12 x y+9 y^{2}+64}=\sqrt{(2 x+3 y)^{2}+64} \geq 8$ | 2p |
|  | $\sqrt{4 x^{2}-12 x+25}+\sqrt{4 x^{2}+12 x y+9 y^{2}+64} \geq 12$ and hypothesis $\Rightarrow$ | 2p |
| $\sqrt{4 x^{2}-12 x+25}+\sqrt{4 x^{2}+12 x y+9 y^{2}+64}=12$ | $1 p$ |  |
| Finalization $x=\frac{3}{2}, y=-1$ | $\mathbf{1 p}$ |  |