Question

Решите что нибудь из этой карточки!!

Answer 1

B1. cos a = - sqrt(1-225/289) = - sqrt(64/289) = -8/17

b2. sin x * cosx * tgx - 1 = sin x* cosx * (sinx / cosx) - 1 = sin x* sinx  - 1 = (sin x)^2 - 1 = -(cosx)^2

b3. 2cosx - 1 = 0
2cosx = 1
cosx = 1/2
x = +- arccos(1/2) + 2*Pi*k, k прин Z
x = +-Pi/3 + 2*Pi*k, k прин Z

b4. sin (Pi-x) - sin(Pi/2 - x) + cosx = 0
sinx - cosx + cosx = 0
sinx = 0
x = Pi*k, k прин Z

b5. 6^(1/3) * 18^(1/3) * 4^(1/6) =  6^(1/3) * 18^(1/3) * 2^(1/3) = (216)^(1/3) = 6

b6. 25^(2x-3) = 1/5
5^(4x-6) = 5^(-1)
4x - 6 = -1
4x = 5
x = 5/4

b7. 2^(3x-1) <= 128
2^(3x-1) <= 2^(7)
2x - 1 <= 7
2x <= 6
x<= 3

b8.
ОДЗ: 9x - 41 >=0
9x >= 41
x>= 41/9

sqrt(9x-41) = 13
9x - 41 = 169
9x = 169 + 41
9x = 210
x = 210/9 = 23 1/3

b9. ОДЗ:
-3/(9x-7x) > 0
-3/2x > 0 | * (-2/3)
x < 0

sqrt(-3/(9x-7x)) = 1/5
-3/(9x-7x) = 1/25
-3/2x = 1/25 | * (-2/3)
x = -2 / 75

b10. 
ОДЗ 
{7x + 8 >= 0
{x >= 0

{x >= -8/7
{x >= 0

x >= 0

sqrt(7x+8) = x
7x + 8 = x^2
x^2 - 7x - 8 = 0
D = 49 - 4*1*(-8) = 81
x1 = (7 + 9) /2 = 16/2 = 8
x2 = (7 - 9) /2 = -2/2 = -1 - не удовл ОДЗ

с1. 
cos2x + 8sinx = 3
1 - 2 (sinx)^2 + 8sinx - 3 = 0
 -2 (sinx)^2 + 8sinx - 2 = 0 | : (-2)
(sinx)^2 + 4sinx + 1 = 0 
sinx = t, -1 <= t <= 1
t^2 + 4t +1 = 0
D = 16 - 4 = 12
t1 = (-4 + 2sqrt(3)) / 2 = -2 +sqrt(3)
t2 = -2 +sqrt(3) не принадлежит промежутку [-1;1]
sinx = -2 +sqrt(3)
x = (-1)^k arcsin (-2 +sqrt(3)) + Pi*k, k принадл Z