Наименьшее натуральное число

1.

НОК (4;6;7) 12 7 84
1

2.

2 0 5
x
2 x
1
2

3.

ОДЗ :
6 x 5
тогда
( x 6)(5 x) x 6,3 x 5,7 12 2 6
x 2 x 30 24
x2 x 6 0
6 5 4 3 4 5 3
3

4.

4

5.

5

6.

b1 q 2 b1 q 1600
b1 q (q 1) 1600
3600
3
2
q
q
4
3
3
1600
2
b1 q (q 1) 3600
b1 q b1 q 3600
b1 q 5 b1 q 4 b1 q 4 (q 1) b1 q 3 (q 1)q 3600
3
5400
2
6

7.

x 3 6 x (3 2 3 4 ) 3 6 x 2 4 3 3 2 3 4 x 6 x 6
7

8.

(cos x 4 cos x 4 1)
2
1
1
(cos x 2) 2 1
3 cos x 2 1
1 (cos x 2) 2 9
2 (cos x 2) 2 1 10
1
1
1
2
10 (cos x 2) 1 2
8

9.

( x 2)(5 x) 0
( x 1)( x 2) 1
x2 x 3 0
x1, 2
1 13
2
3 13 4
2
1 13
2,5
2
1,5
1 13
1
2
2 3 4 5 10
9

10.

10

11.

11

12.

12

13.

x2 x 2 0
6 2 n
x
5
2 n
6
1 5
1
6 6
13

14.

1 y
(x ) 3
3
1
1
2
log 3 ( x )
3
y
2
1
y
1
1
y
x 3 3 1
1 y
0
y
y ( ; 1] (0; )
14

15.

0,6 B
0,6 B
100%
100% 20%
B 0,25B
B
15

16.

sin
2tg
2
1 tg 2
1 tg 2
/2
0
1 2 / 16
2
2 1 / 16 0
cos
1 2 / 16
2
1 tg
2
2
16

17.

17

18.

( x 1) 2 ( y 1) 2 2
x y C
x 2 (C x) 2 2 x 2(C x) 0
2 x 2 2Cx C 2 2C 0
D
C 2 2C 2 4C C 2 4C C (C 4) 0
4
x y Cmax 4
18

19.

19

20.

y 2 xy 2 x 2 0
( x 3)( x 5) 0
9 15
S
2 24
2
20

21.

2 a 30 31 cos 0 0
2 32
a 5
a
21

22.

22

23.

23

24.

arctg
4
4
3
arcsin arccos
3
5
5
3
4
y 3 sin( x ) 4 cos( x ) 5( sin( x ) cos( x ))
5
5
5(cos sin( x ) sin cos( x )) 5 sin x
2
1
5
x [ ; ] sin x [ ;1] 5 sin x [ ;5]
6 3
2
2
24

25.

1) 2 x a 2 x 2a 5
x1 3a 3
2) 2 x a 2 x 2 a 5
a 7
x2
3
x1 x 2
a 7
1 2 3a 3
a 1
2
3
25

26.

x
1
log2 x
x log2 12
x
logx 2 x log2 12
2 x 2 log2 12 12 2 x
(2 x ) 2 12 2 x 32 0
2x 4 2x 8
x 2 x 3
26

27.

D
4 0
(a 2) 2 a 2 3a 4 0
b
4
a 2 4
2
a
16 4(2a 4) a 2 3a 4 0
f
(
4
)
0
a 8
a 8 0
a 6
a 6
a 2 11a 28 0
(a 4)( a 7) 0
27

28.

x y n
y x n
x 2 ( x ) 2 a 2 0
2 x 2 2 x 2 a 2 0
D
2 2( 2 a 2 ) 2 2a 2 0
4
a
2
2
2
28

29.

log 4 x log4 7 log 4 (49 8 logx 4 )
log 4 7 log 4 x log 4 49 log x 4 log 4 8 | log 7 4 log 4 x
log 24 x 2 log 4 x log 4 8 0
log 4 ( x1 x 2 ) 2
x1 x 2 16
29

30.

30