Question

решите уравнение: $243+ 3^{2x} - 43^{x+2} =0$

Answer 1

$243+ 3^{2x} - 4cdot3^{x+2} =0\\243+ 3^{2x} - 4cdot3^{x}cdot 3^2 =0\\3^{2x}-36cdot 3^x+243=0\\t=3^x textgreater 0\\\t^2-36t+243=0\\t_1=9quadRightarrow 3^x=9;quad x=2\\t_2=27quadRightarrow 3^x=27;quad x=3$