3) 5^(1,3)*5^(-0.7)*5^(1,4) = 5^(1,3 - 0,7 + 1,4) = 5^2 = 25
4) √(7x + 32) = 3 - 2x
[√(7x + 32)]^2 = (3 - 2x)^2
3 - 2x ≥ 0, x ≤ 1,5
7x + 32 = 9 - 12x + 4x^2
4x^2 - 19x - 23 = 0
D = 361 + 4*4*23 = 729
x1 = (19 - 27)/16 = 1/2
x2 = ((19 + 27)/16 = 23, не удовлетворяет условию: x ≤ 1,5
Ответ: х = 1/2
5) log_2(20)*log_2(5) = l[og_2(4) + log_2(5)]*log_2(5) = 2log_2(5) + log^_2(5)
6) cos^2(75) - sin^2(75) = [cos(75) + sin(75)]*[ cos(75) - sin(75)] =
= [√2cos(45 - x)]*[√2sin(45 - x)] = 2* [cos(45 - x)]*[sin(45 - x)] = 1
7) log_2(-x^2 + 4x + 5) = log_2(-31 - x)
ОДЗ: 1. -x^2 + 4x + 5 > 0
x^2 - 4x - 5 < 0, x ∈(-1;5)
2. -31 - x > 0
x < - 31
----///////////////----------------------------////////////////////////////------------------>
-31 -1 5 x
x ∈Ф
^2 + 4x + 5 = -31 - x
x^2 - 5x - 36 = 0
D = 25 + 4*1*36 = 169
x1 = (5 - 13)/2 = - 4 не удовлетворяет ОДЗ
x2 = (5 + 13)/2 = 9 не удовлетворяет ОДЗ
Уравнение решений не имеет.
8) 2sinx + 1 = 0
sinx = -1/2
x = (-1)^(n)*arcsin(-1/2) + πn, n∈Z
x = (-1)^(n+1)*arcsin(1/2) + πn, n∈Z
x = (-1)^(n+1)*(π/6) + πn, n∈Z
9) (x+4)/[(3x+9)*(x-4)] ≤ 0
x1 = - 4, x2 = - 3, x3 = 4
- + - +
---------------------------------------------------------------------------------------------->
-4 -3 4 x
x∈( -≈; -4] (-3;4)
10) √(9 - x^2) * log_3(x^2 + 2x - 23) = 0
1. √(9 - x^2) = 0, ОДЗ: 9 - x^2 ≥ 0, x^2 ≤ 9, x∈[-3;3]
x^2 = 9, x1 = -3, x2 = 3
2. log_3(x^2 + 2x - 23) = 0
x^2 + 2x - 23 = 3^0
x^2 + 2x - 23 =1
x^2 + 2x - 24 = 0
x3 = - 6 ∉ [-3;3]
x4 = 4 ∉ [-3;3]
Ответ: х1 = -3; х2 = 3
lg((3x^2 + 13) / (3x - 5)) = lg10
ОДЗ 3x - 5 > 0, x > 5/3
(3x^2 + 13) / (3x - 5) = 10
3x^2 + 13 = 30x - 50
3x^2 - 30x + 63 = 0
x^2 - 10x + 21 = 0
По теореме Виета х_1 = 3, х_2 = 7
Ответ. 3; 7
A)6:x=x;6/х(запишем в виде дроби)=x;x=x:6/х=х/1•х/6=х/6
Б)6:x-6(перенесли)=-х;1/х=-x;
Otvet:-x
5m^2-5m+4+4m^2-7m+8= 9m^2 -12m+12= 3(3m^2-4m+4)
