Question

Решите неравенсво(ХЕЛП)Задание на фото

Answer 1

(6ˣ-1)(36-6ˣ)>0  
1.
(6ˣ-1)>0    6ˣ >1  6ˣ >6⁰   x>0
(36-6ˣ)>0   36>6ˣ 6²> 6ˣ  x<2
\\\\\\\\\\\\\\
_____0_________2___________
           //////////////////////////////////////////    x∈(0 ;2)

2.

(6ˣ-1) <0    6ˣ <1  6ˣ <6⁰   x<0
(36-6ˣ) <0   36<6ˣ 6²< 6ˣ  x>2

\\\\\\\                       ////////////////////
_______0_________2__________    x∈∅

Ответ :  x∈(0 ;2)

Answer 2

$(6 ^{x} -1)(36 - 6 ^{x} ) textgreater 0$
$6 ^{x} =a textgreater 0$
(a - 1)(36 - a) > 0
- (a - 1)(a - 36) > 0
(a - 1)( a - 36) < 0
   +           -                    +
______________________
        1                 36
        ////////////////////
$6 ^{x} textgreater 1$
$6 ^{x} textgreater 6 ^{o}$
x > 0
$6 ^{x } textless 36$
$6 ^{x} textless 6 ^{2}$
x < 2
Ответ : x ∈ (0 ; 2)