Algevra a Lykeioy Theoria Askiseis

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Algevra a Lykeioy Theoria Askiseis

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1 - - - 2 R :[ .[ .[ , - .[ .[ x + = 0.[ .[ , .[ .[ .[ x + > 0 x + < 0.[ .[ .[ .[ .[ .taexeiola.blogspot.com[ ( ) 0.[ .[ .[ x = .[ .[ .[ , , .[ .[ , 0.[ .taexeiola.blogspot.com11. :) x, (1) , .) (1), - :( ) ( ) (( + + x - x (2) :1 : 0 , (2), :xx` ` 0 , : x = 2 : = 0, (2) : - = 0x (3) = 0, (3) 0x = 0 x, , . 0 , (3) , 1 , , 2 , . x + = 0 - ) 0 x + ; (1)) 0 x + 17. 1 1taexeiola.blogspot.com12. 1:) : ( ) ( ) (( (( + + > + x 0 x x > (1) :1 : > 0. (1) , ( > 0 ) (1) > x x>-2 : < 0. (1) . ( < 0 ). (1) < x x < -3 : = 0. (1) : 0x > -. (2)i) 0 0 < > , (2) x.( (2) 0 )ii) 0 0 , (2) ,( 0 ). . : x + > 0 x + < 0 : 27.0 x ) 0 x ) < + > + 2taexeiola.blogspot.com13. 1: (1) .1 : 0 , (1) .2 : 0 , (1) , 0 0 . (2) : (1) (2) 31.A: 3. - (1) (2). (1) (2) : : 22 33. : 32.: : , 0 =-, < 0 || (1): 2(1)2 22 , 0 0 ( ) (), 0 0| | | < 0 x = - 0 ; 34. 3 4 5 6taexeiola.blogspot.com14. 1:) :( ) ( )||||

+ 0 0 2 2 2 22 2) () < 0 0 x x = 0 x = 0.:) 1 : x ( x) x < : < < < < 0 - x x x x2 2 2 2 22 ( )( ) 0 x - x < + (1) (1) x - , x + :x - < 0 x + > 0 ( x - < x + ). x 0 x x 0 x < < + > > : : (1) x < < 2 : : x 0 x x : x x x - (x 0 - 0) < < > < ) 0 0 x ( x x x x: x x 0 x> < > < < :) > 0 x x < < < ) > 0 x x x < > > < 0; 35.x 7taexeiola.blogspot.com15. 1 : x x < < < : 0 , x x > ) 1 : : > > > > 0 x x x x2 2 2 2 22 ( ) ( ) 0 x x > + (1) (1) x - , x + . : x 0 x x 0 x > > + > > : : x > . x < 0 x < x + < 0 x < .: : x < -. x : |x| > x > x < -.2 : : x x : x x 0 x > > x 0 x x : x x x - < > > < : - x x x < > >3 : x > x x . x x : x x - x > < . x > x - x > < . < 0 : x < R x (). x > R x . : - x x x , > 0xxtaexeiola.blogspot.com16. 1:)1 : 22 , () :( ) ( )2 2 2 2 2 2 2 2 2 .2 : , : , 0 , 0 : ,( ) ( )0 , 0 : 0, 0( ) , 0 : 0, 0( ) , 0 : ) () :) )

36. , : + + . ;: + , + :( )2 2 + + 2 2 2 + + +2 (1) ( )2 2 2 2 22 2 2x x . , , + + . 37. 8 9taexeiola.blogspot.com17. 1 , ; 38. . (1) :( )2 2 2 2 2 2 22 2 2| | + + + + + + + 2 2 x x R x . 0 . , .: : + : , d(, ) .: ( ) , d taexeiola.blogspot.com18. 1 10 10 11 taexeiola.blogspot.com19. 1 12 13taexeiola.blogspot.com20. 1 14 15 16taexeiola.blogspot.com21. 1 17 18taexeiola.blogspot.com22. 2 : . 22-23: : 5, 6, 7 : 1, 4. 27-28: : 1, 2, 3 : 1, 4. 36-37: : 1, 4, 10, 11 : 1. 42-43: : 1, 2, 3, 6, 7, 8, 9, 10, 11 : 2. 49-51: : 4, 5, 7, 8, 9, 10, 13, 16, 17, 18. 121-122: : 1, 2, 3, 4, 5. 125: : 1, 2, 3, 7. 128: : 1, 2, 3, 4, 5, 6 : : 31, 32, 42, 44,54, 62, 67 : 74, 81, 86, 89,95,101,105,122, 134,139 1 "" 2taexeiola.blogspot.com23. 3 1 2 31. : ( ) ( )22x 1 5 10x : x .( ) ( )22x 1 5 10x 2 22 x 50x 5 2 22 x 50x 5 ( ) ( )2 22 50 x 5 1 : 22 50 0 ( )22 25 0 ( )( ) 2 5 5 0 + 5 0 5 0 + 5 5 .. 5, 5 (1) :( )( )( ) ( )22 5 5 x2 50 2 5 5 2 5 + +. 5 (1) 0x 0 , ( ). 5 (1) 0x 50 , .2. : x x 1 x 312 3 6+ : , 6.x x 1 x 36 6 6 62 3 6+ ( ) ( ) ( )3 x 2 x 1 6 x 3 + 3x 3 2x 2 6 x 3 + + + 3x 2x x 6 3 2 3 + + ( )3 2 x 3 7 + + ( ) ( ) 3 x 3 7 1 + + 3 0 + 3 .taexeiola.blogspot.com24. 3. 3 (1) :3 7x 3 +

+. 3 (1) : 0x 2 , .3. : ( )( ) 3 x 1 3 2x 4 :( )( ) 3 x 1 3 2x 4 ( )2 2 3 x 2x 3 3 4 + + ( ) ( )2 2 3 2 x 4 1 + :2 3 2 0 + ( )3 12 3 12 2 1 . 1, 2 (1) :( )( )( )( )22 4 2 2 2x 3 2 1 2 1 + + + . 1 (1) : 20x 1 4 0x 3 . 2 (1) : 20x 2 4 0x 0 .4. 36 .: xy , : ( ) ( ) x10 y y10 x 36 + + (1) x 3y (2). (2) :x10 y 30y y 31y + + y10 x 10y 3y 13y + + (1) : 31y 13y 36 18y 36 y 2 . x 6 , 62.5. :i. 2 2x 1 5 ii. x 1 2 1 x 513 2 taexeiola.blogspot.com25. 3iii. 2 x 1 3x 4 iv. 2x 1 9 :i. 2 2x 1 5 2 2x 1 5 2 2x 1 5 2x 1 3 2x 1 7 2x 1 3 2x 1 7 2x 1 7 .2x 1 7 2x 1 7 2x 1 7 2x 8 2x 6 x 4 x 3 ii. x 1 1 x ( ), : 2 5 2 51 6 6 6 2( 2) 6 3( 9)3 2 3 2 2 4 6 3 15 5 5. x 1 5 x 1 5 x 1 5 x 6 x 4 .iii. 2 x 1 3x 4 : x 1 , x 1x 1x 1 , x 1 | + | x 1 :62( x 1) 3x 4 5x 6 x5 + , (). x 1 :2(x 1) 3x 4 x 2 x 2 ( ).iv. : 2() 9 ( 3)( 3) + - : 3 3 +()+ + taexeiola.blogspot.com26. 3 : 1. ( 3, 3) 2 9 0 < , () .2. 3, 3 2 9 0 () : x 1 0 x 1 .3. ( , 3) (3, ) + 2 9 0 > , () : 2 2 22x 1 9 x 1 9 x 1 9x 8 10 + +2 x = 6. : i. x 2 1 x 2 212 3 < ii. 2 3x 1 8 < < iii. 2 x 1 3 < iv. 2x x 1 x 5 + + < +:i. x 2 : 1 2 1 21 6 6 6 3( 1) 6 2( 2)2 3 2 3 < < < 13 133 3 6 2 4 5 13 x 25 5 < + < < < 13 13 13 13 3 26x 2 2 x 2 x5 5 5 5 5 3< < < < + < < .ii. 3x 1 82 3x 1 83x 1 2| ||3x 1 88 3x 1 87 3x 97x 33 < < < < < < < 3x 1 23x 1 2 3x 1 23x 1 3x 31x x 13 > < >< >< > : 7 1x 1 x 33 3 < < < < .taexeiola.blogspot.com27. 3iii. 2 x 1 3 3x 2 x 1 3 5 x 1 15 x 1 1. x 1 5 5 x 1 5 4 x 6 < < < < < > > < < < < x , 2 2x x 1 x x