Question

Ajutor! Exercițiile 35, 36, 37,38,39,40,41,42,43,44
Dau coroana!

Answer 1

35)   x = 5  si   a + b = 13

a) 3 · x + 7 ·a + 7·b = 3 ·x + 7 (a+b) = 3·5 + 7×13 = 15 + 91 = 106

b) x·a + x· b - 50 = x (a + b) -50= 5 · 13 - 50 = 65 - 50 = 15

c) 10 · x - ( 4· a +4 · b)= 10 · x - 4 (a + b) =10 ·5 + 4 ·13 = 50 + 62= 112

d)

(4a + 4b - 2x )· ( 2a + 2b + x)= [4(a + b) -2x]·[2(a + b) + x]

=(4·13 - 2·5) · (2·13 + 5)=(52 - 10)·(26 + 5) = 42·31 = 1302

36

a)x + 3 (a - b) =20⇒ x +3·6 = 20⇒ x= 20 - 18 ⇒x = 2

b) x·a-x·b+9a-9b=654

x(a-b)+9(x-b)=654

x·6 + 9· 6 = 954

x·6 = 954 -54

x=900:6

x= 150

c) 7(a - b) + x = 55

7 · 6 + x = 55

42 + x = 55⇒ x = 55 - 42 ⇒ x = 13

d)

13 + x - 5(a - b) = 2011

13  x - 5·6 = 2011

x = 2011 + 30 - 13

x = 2028

37

a + b + c = 57

a + a + b + c + c = 76,

57 + a + c = 73, a + c = 16

(a + c)·(5a + 2b + 5c) =

= (a + c)·(2a + 2b + 2c + 3a + 3b)=

= (a + c)·[2(a  + b + c) + 3(a + c)]

= 16 · (2·57 + 3·16)=

= 16 ·  (114 + 48)=

= 16 · 162

= 2592

38.

a)

3a + 7b + 4c putem scrie ca :

a + b + a + b + a + b + b + c + b + c + b + c + b + c = 20·3 + 30·4

= 60 + 120 = 180

b) 5a+3b+2c putem scrie ca :

a + b + a + b + a + b + a + c + a + c = 33·3 + 11·2 = 99 + 22 = 121

39. x + 3y = 2y + z = 14

a) x+3y=14  si  2y+z=14

x + 3y + 2y + z= x + 5y + z = 14 + 14 = 28

b) 3x + 15y + 3z = 3(x + 5y + z) = 3·28 = 84

c) 5x + 11y - 2z = 5x + 15y - 4y - 2z = 5(x + 3y) - 2(2y + 2) = 5·14 - 2·14 = 3·14 = 42

d)5x + 19y + 2z = 5x + 15y + 4y + 2z = 5(x + 3y) + 2(2y + z) = 5·14 + 2·14 = 7·14 = 98

40.

a·b=672⇒b=672/a

(a+10)·b = 992 ⇒(a + 10) ·672/a = 992

672a + 6720 = 992a⇒672 a - 992a = - 6720⇒-320a = -6720

320a = 6720⇒a = 21

b = 672/21⇒ b = 32

41.

a × b = 1530 si  a×(b - 20) = 850  ⇒  a×b - 20a = 850

    1530 - 20a = 850 ⇒ 20a = 1530 - 850 = 680 ⇒  a = 680:20= 34

  b = 1530:34 = 45 Deci a = 34 si b = 45

42.

a · b · c = a·b + 48

48 = 2a · 2b

a·b = 48:4

a·b = 12⇒a = 12:4    

               ⇒ a = 3

b = 12:3    ⇒  b = 4

3·4·c = (3·4) + 48

12·c = 12 + 48⇒12·c = 60⇒c = 60:12

               ⇒ c = 12

43

$11+8 \cdot\left[45+4\left(3+8\left(12\cdot \:13-8\cdot 14\right)-37]+1234=$

$8\cdot [45+4\left(3+8\left(156-112)-37]=10536$

11+10546+1234=

=11781