Решите уравнение 4^x+1-13*6^x+9^x+1=0

$4^{x+1}-13\cdot 6^x+9^{x+1}=0\\\\4\cdot 4^x-13\cdot 6^x+9\cdot 9^x\\\\4\cdot 2^{2x}-13\cdot 2^x\cdot 3^x+9\cdot 3^{2x}=0\\\\\\\text{Delim vse na } 2^x\cdot 3^x\\\\\\4\cdot \dfrac{2^x}{3^x} -13+9\cdot \dfrac{3^x}{2^x} =0\\\\\\t:= \bigg(\dfrac{2}{3} \bigg)^x \geq 0\\\\\\4t+ \dfrac{9}{t} -13=0$

$4t+ \dfrac{9}{t} -13=0\\\\4t^2-13t+9=0\\\\D=25\\\\t_1= \dfrac{13+5}{8} = \dfrac{9}{4} ;\quad t_2=1$

$\bigg(\dfrac{2}{3} \bigg)^x= \dfrac{9}{4}\\\\\bigg(\dfrac{2}{3} \bigg)^x= \bigg(\dfrac{2}{3}\bigg)^{-2}\\\\x=-2$

$\bigg(\dfrac{2}{3} \bigg)^x=1\\\\x=0$