0\\\\3\cdot (\frac{3}{2})^{4x}+(\frac{3}{2})^{2x}-2=0\\\\t=(\frac{3}{2})^{2x}>0,\; \; 3t^2+t-2=0\\\\D=25,\; \; t_1=\frac{-1-5}{6}=-1,\; \; t_2=\frac{-1+5}{6}=\frac{2}{3}\\\\(\frac{3}{2})^{2x}=-1<0\; \; net\; reshenij\\\\(\frac{3}{2})^{2x}=\frac{2}{3},\; \; \frac{2}{3}=(\frac{3}{2})^{-1}\\\\2x=-1,x=-\frac{1}{2}" alt="1)\; \; 3^{4x+1}+6^{2x}-2^{4x+1}=0\\\\3\cdot 3^{4x}+3^{2x}\cdot 2^{2x}-2\cdot 2^{4x}=0\, |:2^{4x}>0\\\\3\cdot (\frac{3}{2})^{4x}+(\frac{3}{2})^{2x}-2=0\\\\t=(\frac{3}{2})^{2x}>0,\; \; 3t^2+t-2=0\\\\D=25,\; \; t_1=\frac{-1-5}{6}=-1,\; \; t_2=\frac{-1+5}{6}=\frac{2}{3}\\\\(\frac{3}{2})^{2x}=-1<0\; \; net\; reshenij\\\\(\frac{3}{2})^{2x}=\frac{2}{3},\; \; \frac{2}{3}=(\frac{3}{2})^{-1}\\\\2x=-1,x=-\frac{1}{2}" align="absmiddle" class="latex-formula">
0,\; \; 9t^2+26t-3=0,\\\\D/4=13^2-9\cdot (-3)=196,\sqrt{D}=14\\\\t_1=\frac{-13-14}{9}=-\frac{27}{9}=-3<0,\; ne\; podxodit,\; t_2=\frac{1}{9}\\\\3^{x+\frac{1}{x}}=\frac{1}{9},\; \; 3^{x+\frac{1}{x}}=3^{-2}\\\\x+\frac{1}{x}=-2,\; \; x+\frac{1}{x}+2=0,\; \; x^2+2x+1=0,\; \; (x+1)^2=0\\\\x=-1" alt="2)\; \; 9^{x+\frac{1}{x}+1}+26\cdot 3^{x+\frac{1}{x}}-3=0\\\\9\cdot (3^{x+\frac{1}{x}})^2+26\cdot 3^{x+\frac{1}{x}}-3=0\\\\t=3^{x+\frac{1}{x}}>0,\; \; 9t^2+26t-3=0,\\\\D/4=13^2-9\cdot (-3)=196,\sqrt{D}=14\\\\t_1=\frac{-13-14}{9}=-\frac{27}{9}=-3<0,\; ne\; podxodit,\; t_2=\frac{1}{9}\\\\3^{x+\frac{1}{x}}=\frac{1}{9},\; \; 3^{x+\frac{1}{x}}=3^{-2}\\\\x+\frac{1}{x}=-2,\; \; x+\frac{1}{x}+2=0,\; \; x^2+2x+1=0,\; \; (x+1)^2=0\\\\x=-1" align="absmiddle" class="latex-formula">