3 x − 4 3 x + 1 = − 9 {\displaystyle 3^{x}-4{\sqrt {3^{x+1}}}=-9}
3 x − 4 3 x + 1 = − 9 ( 3 x + 9 ) = 4 3 x + 1 ( 3 x + 9 ) 2 = 4 2 ( 3 x + 1 ) 3 x = t ( t + 9 ) 2 = 16 ( 3 t ) t 2 + 18 t + 81 = 48 t t 2 − 30 t + 81 = 0 ( t − 27 ) ( t − 3 ) = 0 t = 27 t 2 = 3 3 x = 27 3 x = 3 3 x = 3 3 x = 1 x = 3 x = 1 {\displaystyle {\begin{aligned}3^{x}-4{\sqrt {3^{x+1}}}=-9\\(3^{x}+9)=4{\sqrt {3^{x+1}}}\\(3^{x}+9)^{2}=4^{2}(3^{x+1})\\3^{x}=t\\(t+9)^{2}=16(3t)\\t^{2}+18t+81=48t\\t^{2}-30t+81=0\\(t-27)(t-3)=0\\t=27\ \ \ \ \ t_{2}=3\\3^{x}=27\ \ \ \ \ \ \ 3^{x}=3\\3^{x}=3^{3}\ \ \ \ \ \ \ x=1\\x=3\ \ \ x=1\\\end{aligned}}}
