Решите уравнение [latex] -\frac{4}{9} +( \frac{2}{3}) ^{2x} +52 ^{x} * 3^{-x-2} =0[/latex]

-4/9+(2/3)^(2x)+5*(2^x)*(3^(-x-2))=0 5*(2^x)*(3^(-x-2))=5*(2^x)*((1/3)^(x))*(1/3)^²=5*((2/3)^x)*(1/9)=(5/9)*((2/3)^x) -4/9+(2/3)^(2x)+(5/9)*((2/3)^x)=0 |*9 -4+9*((2/3)^(2x)+5*((2/3)^x)=0 (2/3)^x=t, t>0 9t²+5t-4=0 D=25+144=169 t₁=-1, -1<0.  не подходит t₂=4/9 (2/3)^x=4/9 (2/3)^x=(2/3)² x=2