Решите неравенство (log2^2 x - 2log2 x )^2 + 36log2 x + 45 меньше 18log2^2 x

[latex]\displaystyle (log_2^2x-2log_2x)^2+36log_2x+45\ \textless \ 18log_2^2x[/latex] [latex]\displaystyle (log_2^2x-2log_2x)^2-18(log_2^2x-2log_2x)+45\ \textless \ 0[/latex] [latex]\displaystyle Log_2^2x-2log_2x=t[/latex] [latex]\displaystyle t^2-18t+45\ \textless \ 0[/latex] [latex]\displaystyle D=324-180=144=12^2 t_P1=15; t_2=3[/latex] __+_____-_____+____           3                15 [latex]\displaystyle \left \{ {{Log_2^2x-2log_2x\ \textless \ 15} \atop {log_2^2x-2log^2x\ \textgreater \ 3}} \right. [/latex] 1)  [latex]\displaystyle log_2^2x-2log_2x-15\ \textless \ 0[/latex] [latex]\displaystyle D=4+64=64=8^2 [/latex] _+____-_____+____     -3              5 [latex]\displaystyle -3\ \textless \ log_2x\ \textless \ 5[/latex] [latex]\displaystyle \frac{1}{2^3}\ \textless \ x\ \textless \ 2^5 [/latex] 2) [latex]\displaystyle log_2^2x-2log_2x-3\ \textgreater \ 0[/latex] [latex]\displaystyle D=4^2[/latex]  __+___-____+___        -1        3 [latex]\displaystyle \left \{ {{log_2x\ \textgreater \ 3} \atop {log_2x\ \textless \ -1}} \right. [/latex] [latex]\displaystyle \left \{ {{x\ \textless \ \frac{1}{2}} \atop {x\ \textgreater \ 2^5}} \right. [/latex] Объединим все промежутки с учетом ОДЗ х>0    \\\\\\\\\\\\\\\\\\\\\             \\\\\\\\\\\\\\\\\\\\\\\\\\\\             //////////////////////////////////////   0      1/8      1/2          8          32 ОТВЕТ: (1/8; 1/2) ∪(8;32)