  .      
 


       ?      :      .     :         .90     .        .      ,           .





  

     



 



 ,2022



ISBN978-5-0059-3155-9

     Ridero







   ,   :    .   .

 ,    ,      .    ,    .    ,     ,  .        ,     ,     .   :  !    !  .  ,    !      ,     .     ,     ,   ;      .

  - ,    ?  !  !




  



ࠖ   .     ,   ,  .     ,   :    ,  . ,     .    :  , ,  .        :

2+3= 5 7 4=3

 ,  ,       ,  .

  : a+ b = c  c a= b.     ,       .   ,     .

  : 4+8=12

     .

4+8+3=12

  ?

15=12

 !   ?       ,      .

4+8+3= 12+3.   ? 15=15

    .   :          ,      .      ,   :

 a+ b = c,  a+ b + n = C + n,  a, b, c, n   .

 ? !     .

 ,       ?

5+2=7

5+25=7

  ? 2=7

 ,   ,   .          .

5+2 5= 7 5.  2=2.

  !     .   :         ,      .

   :

 a+ b = c,  a+ b n = c n,  a, b, c, n   .

      ?        .  :

5 1=4

 ,      7?

(5 1) 7= 4,  28=4

 .      7.

(5-1) 7= 4 7.  28=28

      .   :

         ,      .

 a b = c,  (a b) n = (c)n

  .  ,      ?

4+6=10

(4+6) /2= 10,  5=10.

   :        ?

  ,    .

        .

(4+6) / 2= 10/ 2,  5=5

    .   :

         ,     .

,   :

 a+ b = c,  (a+ b) /n =c/n

 a, b, c  , n  0,      0.

  :       ?

   :         .

 ,    .

ՠ 3=11

     ?    :

         ,    .      3  .

ՠ 3+3= 11+3

 -3+3=0

  = 11+3

,=14



   ,     .

		ՠ b =

  ,    

		ՠ b + b = +b
		  -b + b = 0,
		 = +b.

   X + b = c,     .

		 X + b = c,
		 + b b =  b 
		 = 񠖠b.

 :  +7=15

 7  :

		 +7 7= 15 7 =8

 ,    1.




 1.  


 :

		1. X 5=0
		2. X +11=3
		3. X ab =4
		4. X Y =Z
		5. X 2a =c
		6. X +3ab =bc
		7. X + k = 1+k
		8. X ab = aab
		9. X + c = cb
		10. X 2a = aab
		11. X + cb = 3cbc
		12. X 5+ a= 2a5
		13. X +3 k = 63k
		14. X 1 ab = ab1
		15. X a b = ab
		16. X +2a 3c = 3a2c

     1.    ,   .

     ,   2.

  

		4ՠ 5=15

    .

		4ՠ 5+5= 15+5,  4 =20.

  ?     .

       ,      .

		4/4=20/4, =5.

  

		X b =

  .

		ՠ b + b = +b,
		
		X = +b

   .

 aX = c + b,  aX/a= (c + b)/a

 X = (c + b)/a

 ,    2.




 2.  


 :

		1. 2X 3=5
		2. 3X 5=4
		3. 5X +6=36
		4. 8X 5=43
		5. 7X 2=19
		6. 4X +8=20
		7. 6X a=2a
		8. 2X + b =13b
		9. 7X +3a = a+b
		10. 4X 2a = 4+2a
		11. 4X 3a =a
		12. 3X 2b = 614b
		13. 6X 2a = 24b20a
		14. aX 3a = ab2a
		15. 2aX + ab = 2aab
		16. 3aX c = 3ac7c

 1.

 2.

    :

		/ࠖ 5=6

   :

		/ࠖ 5+5= 6+5
		/= 6+5
		/=11

   .

		/* = 11*
		 =11

  :

		2X 4b =2bc

  :

		2ՠ 4b +4b = 2bc+4b,
		 2X = 2bc+4b

    2:

		2/ 2= (2bc +4b) /2

  ,    .

  ,     .

   

		(2bc+4b) /2= 2bc/2+4b/2

 . ,  c = 2b =3.

   2,     2

		2*3*2/2+4*3/2=12

    ,   2.

		(2*3*2+4*3) /2,  24/2=12

   .  ,

		(+ b) /2= /2+b/2.

  :    ,       .   .

		2 = 2b +4b. :
		2/2=2b/2+4b/2
		: X = bc+2b

    b  X = b (c+2)

 ,    ,         .     .

   :








5X 5=50X

 2- ,  5X  :

		5X 5 5X = 50X5X
		5=45X
		or 45X =5

    45.

45X/45= -5/45

X =1/9

 :








  堖  (+ )   (+ ).    , 



(+ ) / (+ ) =1


  :








:








 - + b  :








    (a+b)








 b bX = c (a+b)

 2- ,  b   :



b bX b =c (a+ b)b



 -bX =c (a+ b) -b    b:








      ,    (-1).








   ,   (-1) / (-1) = 1.      1,  .















 :

		2 = ࠖb

    2.

     .

    -1

		(-2X) (-1) = (a b) (-1),   
		2 =  + b  2 = b

    2.








     :

		2 = ࠖb

    -2








     ,      ࠖ1








 :

		3ࠖ 6 = 6ՠ9

  ,      -6X

   +6X.    +  X.    +6X    -6X   .

 6X   :



3ࠖ 6 +6 = 6ՠ 9 +6,   3 = 12ՠ9



 9a   :



3a +9a = 12X 9a +9a  12a =12X



X =a



 ,    3.




 3.  


 :

		1. 1 X = 5a
		2. 1 2X = X4
		3. a 3X = bX
		4. 2a 4X = 2X4a
		5. 4b 2X = 2X4b
		6. ab + aX = 2aX +ac
		7. ab + aX = 2aXac

  : aX bX = ab

   X,       aXbX,

   X (a b) = ab

    ab

		X (a b) / (a b) = (a b) / (ab)
		X =1

 ,    4.




 4.  


 :

		1. bX 2b = aX2a
		2. b 2bX = a2aX
		3. aX bX =1
		4. aX bX cX = 2a 2b2c
		5. 3abX 5a = 3acX+13a
		6. aX bX = acbc
		7. 9a 4X = 5a2X
		8. X aX = 22a
		9. aX bX = ba

  : aX bX = 2b2a

  X   .

		 (ࠖ b) = 2b2

  2  .

		X (a b) = 2(ba)

   (ab).

  -1













      ,   (-1) 









 5.  


 :

		1. 5aX 5bX = 10b10a
		2. aX bX cX = c + ba
		3. 2X 3aX = 6a4
		4. 3aX 9bX = 27b9a
		5. 4bX cX = 8c32b
		6. abX acX = acab
		7. X/2 aX = 12a
		8. aX/5+2a = 5a4aX

     1 2.




 



  X + Y = 3. X Y .     X,  Y  .     ᠫ  .       . : X Y = 1.     2- :

		1. X + Y =3
		X Y =-1

    .  :  X  , , .

   Y   :

		 + Ӡ Ӡ= 3 ; 
		 = 3

  (3 Y)  X   (X Y =-1).

 : 3 Y Y = -1 3 2Y =-1

     Y.  2Y   .

		3 2Y +2Y = -1+2Y
		3= -1+2Y

 1  .

		3+1= -1+1+2Y
		4=2Y

  42Y.

		2Y =4

    2.

		2Y/2=4/2
		Y =2.

  2 Y   ,  X.

  : X + Y =3.

		 +2=3;

 2  .

		+2 2=32;
		 =1
		Y =2

  :

		1.  + Ӡ=3
		ՠ Ӡ=-1

           .

		X + Y = 3X Y = -1
		( + Y) + (ՠ Y) = 3+(-1)

    :








 2 = 2  =1

 1 X  .

		1+ Ӡ=3

 1  .

		1+ Y 1= 31
		Y = 31
		Y=2

    ,   .     ,     .       X Y,   .

    ,      :

		Y =  +b

  : X + Y=3

 X   

		ՠ  + Ӡ= 3 
		Y = 3

  ,      .    X  Y.

		 = 3; Y (3) = 3 3=0
		 = 6; Ӡ(6) = 3 6=3

      .

     .

   .

		ՠ Ӡ=-1

 X   .

		ՠ ՠ Ӡ= 1 ՠ Ӡ= 1

   -1

		Y (-1) = (-1) (-1) X(-1)
		Ӡ= ՠ+1

  ,      .    X  Y.

		 = 5; Y (5) = 5+1=6
		 = -5; Y (-5) = 5+1=-4

       .

 1 ,      X =1

Y=2.

   ,    .






 1.   : X=1,Y=2.



  :

		2. 2 + Ӡ=5
		 + Ӡ=2

     +  X Y  .

     ,      .

(2X + Y) (X + Y) = 5 2=3:








 3 X   .

		3+ Ӡ=2

 3  .

		3+ Y 3= 23
		Y = 2 3=1
		Y =-1
		:  = 3; Y =-1;

    .

 : 2X + Y =5.

   : Y = aX +b

 2X   .

		2X 2X + Y = 5 2X
		Y = 52X

  ,    .    X  Y.

		 = 0; Y (0) =52*0; Y (0) =5
		 = 4; Y (4) = 5 2* 4= 5 8=3

     .

		 + Ӡ=2

    Y = aX +b.

		ՠ  + Ӡ= 2;
		Y = 2

  ,    .    X  Y.

		 = 4; Ӡ(4) = 2 4=2
		 = 4; Y (-4) = 2 (-4) = 2+4=6

 2 ,     (3, -1).  ,    : X = 3, Y =-1.






 2.   : X=3, Y=-1.



  :




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