Question

найдите сумму целых решений неравенства

Answer 1

$left(3^{2x+1}-26cdot3^x-9right)cdotlog^2_3(6-x) textgreater 0\O.D.3:;6-x textgreater 0Rightarrow x textless 6\\1)log^2_3(6-x)=0\6-x=1\x=5\log^2_3(6-x) textgreater 0;npu;xin(-infty;;5)cup(5;;+infty)\\\2);3^{2x+1}-26cdot3^x-9 textgreater 0\3cdot3^{2x}-26cdot3^x-9 textgreater 0\3^x=t,;3^2x=t^2,;t textgreater 0\3t^2-26t-9 textgreater 0\3t^2-26t-9=0\D=676+4cdot3cdot9=676+108=784=(28)^2\t_{1,2}=frac{26pm28}6\t_1=9\t_2=-frac13;-;He;nogx.\3^x=9\3^x=3^2\x=2\3cdot3^{2x}-26cdot3^x-9 textgreater 0;npu;x textgreater 2\KOPHu:;3;u;4\3+4=7$