![image](https://tex.z-dn.net/?f=%7B2%7D%5E%7Bx%7D++%2B+2+%5Ctimes+%7B2%7D+%5E%7B+-+x%7D++%3D+3+%5C%5C++%7B2%7D%5E%7Bx%7D++%3D+t+%3E+0+%5C%5C+t+%2B+2+%5Ctimes++%5Cfrac%7B1%7D%7Bt%7D++%3D+3+%5C%5C++%7Bt%7D%5E%7B2%7D++%2B+2+%3D+3t+%5C%5C++%7Bt%7D%5E%7B2%7D++-+3t+%2B+2+%3D+0+%5C%5C+d+%3D+9+-+8+%3D+1+%3E+0+%5C%5C+x1+%3D++%5Cfrac%7B3+-+1%7D%7B2%7D++%3D+1+%5C%5C+x2+%3D+2+%5C%5C++%7B2%7D%5E%7Bx%7D++%3D+1+%5C%5C+x+%3D+0+%5C%5C++%7B2%7D%5E%7Bx%7D++%3D+2+%5C%5C+x+%3D+1)
0 \\ t + 2 \times \frac{1}{t} = 3 \\ {t}^{2} + 2 = 3t \\ {t}^{2} - 3t + 2 = 0 \\ d = 9 - 8 = 1 > 0 \\ x1 = \frac{3 - 1}{2} = 1 \\ x2 = 2 \\ {2}^{x} = 1 \\ x = 0 \\ {2}^{x} = 2 \\ x = 1" alt="{2}^{x} + 2 \times {2} ^{ - x} = 3 \\ {2}^{x} = t > 0 \\ t + 2 \times \frac{1}{t} = 3 \\ {t}^{2} + 2 = 3t \\ {t}^{2} - 3t + 2 = 0 \\ d = 9 - 8 = 1 > 0 \\ x1 = \frac{3 - 1}{2} = 1 \\ x2 = 2 \\ {2}^{x} = 1 \\ x = 0 \\ {2}^{x} = 2 \\ x = 1" align="absmiddle" class="latex-formula">
Ответ: 0; 1