Найдите значение выражения
1 1/4 + 2/7 - 23/28

А) 2n; Б) 1; В) 8; Г) 3

Объяснение:

А) 23n : 7 для нечётных n = 2k+1

23(2k+1) = 46k + 23 = 42k + 4k + 21 + 2 = 4k + 2 (mod 7) = 2(2k+1) = 2n

Б) 6^12*8^14 = (6^2)^6 * (8^2)^7 = 36^6*64^7 = (35+1)^6*(63+1)^7 = 1^6*1^6 (mod 7) = 1

В) 23^16 + 33^16 + 49^16 = (23^2)^8 + (33^2)^8 + (49^2)^8 = 529^8 + 1089^8 + 2401^8 =

= (510+15+4)^8 + (1080+9)^8 + (2400+1)^8 = 4^8 + 9^8 + 1^8 (mod 15) =

= (4^2)^4 + (9^2)^4 + 1 = 16^4 + 81^4 + 1 = (15+1)^4 + (75+6)^4 + 1 = 1 + 6^4 + 1 (mod 15) =

= (6^2)^2 + 2 = 36^2 + 2 = (30+6)^2 + 2 = 6^2 + 2 (mod 15) = 36 + 2 = 38 = 8 (mod 15)

Г) 3^1255 - 1255^3 = (3^5)^251 - (1200+48+7)^3 = 243^251 - 7^3 (mod 8) =

= (240+3)^251 - 343 = 3^251 - (320+16+7) = 3*3^250 - 7 (mod 8) =

= 3*(3^5)^50 - 7 = 3*243^50 - 7 =

= 3*3^50 - 7 (mod 8) = 3*(3^5)^10 - 7 = 3*243^10 - 7 = 3*3^10 - 7 (mod 8) =

= 3*(3^5)^2 - 7 = 3*243^2 - 7 = 3*3^2 - 7 (mod 8) = 3*9 - 7 = 27 = (24+3) = 3 (mod 8)

а) 7(х - 1) - 12 = 30;

   7x-7-12=30

   7x=30+12+7

   7x=49

   x=49/7

   x=7

б) 3(х - 8) = 4х - 9;

3x-8*3=4x-9

3x-4x=24-9

x=-15

в) 10х - 2(4х - 1) = 19;

10x-8x-2=19

2x=21

x=21/2

x=7.5

г) 13 - х = 6(9 - х);

13-х = 54-6х

6х-х=54-13

5х=41

x=41/5

x=8.2

д) 12 - 3(х - 7) = 5х - 14;

12-3x-21=5x-14

5x+3x=12-21+14

8x=5

x=5/8=0.625

е) 5(х - 3) = -15х - 2(1 - 5х);

5x-15=-15x-2+10x

5x+15x-10x=-2+15

10x=13

x=13/10=1.3

ж) 0,5(х - 3) - 0,3х - 6 = 0,2х - 25;

0.5x-1.5-0.3x-6=0.2x-25

0.5x-0.3x-0.2x=-25+6+1.5

0=32.5 НЕТ РЕШЕНИЙ

з) 0,7х - 0,5(4х + 3) = -2(0,7х - 2);

0.7x-2x-1.5=-1.4x+4

0.7x-2x+1.4x=4+1.5

0.1x=5.5

x=5.5/0.1

x=55

и) 7(0,2х - 1) - 3 (0,1х + 4) = 6(11 - 0,1х);

1.4x-7-0.3x-12=66-0.6x

1.4x-0.3x+0.6x=66+7+12

1.7x=85

x=85/1.7

x=50

к) 0,4(1,5х - 1/4) = 0,6х - 0,1.

0.6x-0.1=0.6x-0.1

0=0    x - любое число