Разложите на множители 5а^4-5а^3-6а+6

группировки
= 5а³(а-1) - 6(а-1)=(а-1)(5а³-6)

1) а) 2^(x + 2) + 2^x= 5
2^x·2^2 + 2^x = 5
2^x(2^2 +1) = 5
2^x·5=5
2^x = 1
2^x = 2^0
x = 0
б) 9^x -6·3^x -27 =0
(3^x)^2 -6·3^x -27 = 0
3^x=t
t^2 - 6t -27 = 0
t = 9                            t = -3
3^x =9                         3^x = -3 
x = 2                            нет решений
ответ: х = 2
 2) 5^(4x -7) больше 1
     5^(4x - 7) больше 5^0
     4x - 7 больше 0
     4х больше 7
     х больше 7/4  
0,7^x меньше 2 2/49
0,7^x меньше 100/49
0,7^x  меньше (0,7)^-2   (0,7 меньше 1)
x больше -2
II вариант
1) а) (2/9)^(2x +3) = 4,5^(х - 2)
(2/9)^(2x+3)меньше  (9/2)^(x - 2)
(2/9) ^(2x +3) = (2/9)^-(x - 2) 
2x +3 = - (х - 2)
2х + 3 = -х +2
3х больше -1
х = -1/3
б) 4^x -14·2^x -32 =0
(2^x)^2 -14·2^x - 32 = 0
2^x =t
t^2 -14t -32 = 0
t = 16                 t = -2
2^x =16             2^x = -2
x = 4                 нет решения       
ответ: х =4
2)а) 2^(2x -9) меньше 1
2^(2x - 9) меньше 2^0   ( 2 больше 1)
2x - 9 меньше 0
2х меньше 9
х  меньше 4,5
б)0,9^x больше 1 19/81
0,9 ^x больше 100/81
0,9^x больше (81/100)^ - 2
0,9^x больше (0,9)^ -2  (0,9 меньше 1)
x меньше -2
III вариант
1)а) 3 ^(x + 2)  + 3^x = 30
       3^x· 3^2 + 3^x = 30
      3^x( 9 +1) = 30
      3^x ·10 = 30
       3^x = 3
       x = 1 
б)9^x - 2· 3^x =63
   (3^x)^2 -2·3^x = 63
   3^x = t
t^2 -2 t - 63 = 0
t = 9                    t =-7
3^x = 9               3^x = -7
x = 2                   нет решений
ответ: х = 2
2)а) 4^ (0,5x^2 -3 )≥ 8
       2^ (x^2 -6)  ≥ 2^3
       x^2 -6 ≥ 3
       x^2 ≥ 9
x∈(-бесконечность; 3] ∨[3; + бесконечность)
IVвариант
1) а) 5^(х +1) - 3·5^(x - 2) = 122
         5^(x -2) ( 5^3 -3) =122
         5^(x - 2)·122 = 122
         5^(x - 2) = 1
         5^(x - 2) = 5^0
           x - 2 = 0 
           x = 2  
б)4^x -3·2^x =40
   2^2x -3·2^x =40
2^x = t
t^2 -3t -40 = 0
t = 8                t = -5
2^x = 8            2^x = -5
x = 3                нет решения.
ответ: х = 3
2) а) 9^ (0,5x^2 -3) меньше 27
        3^x^2 -6 меньше 3^3
        x^2 - 6 меньше 3
         x^2 меньше 9
х ∈(-3; 3)     
б)(√3)^x меньше 9^-0,5
3^ 1/3x меньше 3^-1(3 больше  1)
1/3x меньше -1
х меньше -3

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