[tex]\displaystyle\bf\\3^{x-2}=\left(\frac{1}{3}\right)^{\sqrt{\b{x}}}\\\\3^{x-2}=3^{-\sqrt{x}}\\\\x-2=-\sqrt{x}\\\\x+\sqrt{x}-2=0\\\\Substitutie:~~~\sqrt{x}=y~~~\implies~x=y^2\\\\\\y^2+y+2=0\\\\y_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\y_{12}=\frac{-1\pm\sqrt{1+8}}{2}\\\\\\y_{12}=\frac{-1\pm\sqrt{9}}{2}\\\\\\y_{12}=\frac{-1\pm3}{2}\\\\\\y_1=\frac{-1+3}{2}=\frac{2}{2}=1\\\\\\y_2=\frac{-1-3}{2}=\frac{-4}{2}=-2\\\\\\Ne~intoarcem~la~substitutie:\\x=y^2\\\\x_1=y_1^2=1^2=1\\\\x_2=y_2^2=(-2)^2=4[/tex]
