Question

Пожалуйста, решите неравенство!

Answer 1

$36^{ \frac{x}{x-1} } +2* 6^{ \frac{2x-1}{x-1} } \leq 108$
разделим на 36 

$36^{ \frac{x}{x-1}-1 } +2* 6^{ \frac{2x-1}{x-1}-2 } -3 \leq 0 \\ \\ 36^{ \frac{x-x+1}{x-1} } +2* 6^{ \frac{2x-1-2x+2}{x-1} } -3 \leq 0 \\ \\ 36^{ \frac{1}{x-1} } +2* 6^{ \frac{1}{x-1} } -3 \leq 0 \\ \\ t= 6^{ \frac{1}{x-1} } \\ \\ t^2+2t-3 \leq 0 \\ \\ D=16 \\ \\ t_{1} =-3 \\ \\ t_{2} =1 \\ \\ (t+3)(t-1) \leq 0 \\ \\ ( 6^{ \frac{1}{x-1} } +3)( 6^{ \frac{1}{x-1} } -1) \leq 0 \\ \\ 6^{ \frac{1}{x-1} } \ \textgreater \ 0 \\ ( 6^{ \frac{1}{x-1} } +3)\ \textgreater \ 0 \\ \\ ( 6^{ \frac{1}{x-1} } -1) \leq 0$

$6^{ \frac{1}{x-1} } \leq 1 \\ \\ 6^{ \frac{1}{x-1} } \leq 6^0 \\ \\ 6\ \textgreater \ 1 \\ \\ x \neq 1 \\ \\ \frac{1}{x-1} \ \textless \ 0 \\ \\ x-1\ \textless \ 0 \\ \\ x\ \textless \ 1$

Answer 2

task/28448691
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x /(x-1)= (x-1+1) /(x-1) = 1 +1/(x-1) ;
(2x - 1)/(x-1) = (2x - 2 +1) / (x-1) = 2 + 1 /(x-1) ;