Ερωτήσεις...

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1 1.2 1. ; , . () . 2. ; , . 3. ; , . , . 4. ; ; , . , 0 . 5. ; . 6. ; , . 1.3 7. ; , , , . .

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8. ; ; . , 0 . 9. ; . 10. ; , , . . 1.5 11. ; . 12. .

( + ) = 2 + 2 + 2 2 ( ) = 2 2 + 2 3 ( + ) = 3 + 3 2 + 3 2 + 3 3 ( ) = 3 3 2 + 3 2 32

2 2 = ( + )( )

3 + 3 = ( + ) ( 2 + 2 ) 3 3 = ( ) ( 2 + + 2 )

( + )

2

13. . = ( + )( + ) = ( + )( ) = 2 + 2 == 2 + + + 2 = 2 + 2 + 2

=2 2

( )

2

= ( )( ) = = 2 + 2 = 2 2 + 2

( + ) ( 2 + 2 ) == 3 2 + 2 + 2 2 + 3 = =3 + 3

( + )

3

= ( + ) ( 2 + 2 + 2 ) = = 3 + 2 2 + 2 + 2 + 2 2 + 3 = = 3 + 3 2 + 3 2 + 3

= ( + )( + ) =2

( ) ( 2 + + 2 ) == 3 + 2 + 2 2 2 3 = =3 3

( )

3

= ( ) ( 2 2 + 2 ) = = 3 2 2 + 2 2 + 2 2 3 = = 3 + 3 2 + 3 2 + 3_____________________________________________________________________ : 2

= ( )( )

2

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1.6 14. ; . 15. ; - - ( ) - - x 2 + ( + ) x + 1.7 16. . ( x) = ( x) ( x) + ( x)

( x ) =

( x ) = ( x ) = ( x ) = 1.8 .. ... 17. ... ... ; (...) . (...) . 1.9 18. ; , . 1.1 . 1.4 1.10 .

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2 - 2.1 x + = 0 19. 1 ; 1 ; 1 1. 1 , . 20. x + = 0 . 0 x + = 0 x = = 0 x + = 0 0x = - 0 ( ) - = 0 ( )

.

2.2 21. 2 ; 2 2. 22. x 2 + x + = 0 0 . x 2 + x + = 0 0 > 0 x1,2 = = 0 x = . 2

- < 0 ( ) , = 2 4 23. x 2 + x + 0 ; 1 , 2 x 2 + x + = 0 0 ,

. 2

x2 + x + 2 x + x + = ( x 1 )( x 2 )

2.4 24. ; . 2.5 25. . - > + > + > > > 0 >

>

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- > < 0 <

-

<

> > + > + > > > , , , > > > 2 0

2.3 .

3 3.1 26. x + y = ; x + y = ( x, y ) . 27. ; , . , . 28. y = k ; y = k k 0 xx yy ( 0, k ) , y = 0 xx. 29. x = k ; x = k k 0 yy xx ( k , 0 ) , x = 0 yy. 30. x, y ; x, y x + y = 0 0 . 3.2 31. x, y (2x2) ; 2x2 ( x, y ) . 2x2 ( x, y ) .

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32. 2x2 , ; 2x2 ( x, y ) . ( ). 2x2 . (). 2x2 . ( ). 3.3 .

4 4.1 y = x 2 0 33. y = x 2 0 ; y = x 2 0 . O ( 0, 0 ) ( ) yy. - > 0 xx y = 0 x = 0 . - < 0 xx y = 0 x = 0 . y = x 2 xx . , . 4.2 y = x 2 + x + 0 34. ; y = x 2 + x + 0 35. y = x 2 + x + 0 ; y = x 2 + x + 0 2 , , = 4 2 4 x = -

. 2

> 0 y = x 2 + x + y = x =

. 2

4

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- < 0 y = x 2 + x + y = x=

4

-

. 2

5 5.1 36. ; . . 37. ; (, , , ,). , , . : - , = {2, 0, 4} = { , , , , } = { } = { x , x } Venn

38. ; ; . , . . 39. , , . . , . . , . . = = .

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5.2 - 40. ; . 41. , ; . , . , . 42. ; = . 5.3 43. ; , , ( ) ( ) = . = ( ) 44. . 0 ( ) 1 . ( ) + ( ) = 1 . , ( ) + ( ) = ( ) + ( ) .

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1 1.1 1. ; ( ), ( ) ( ). ( ), ( ) ( ). 2. , , ; . , . . 3. . 1 ( ) , . 2 ( ) , . 3 ( ) , . 4. . , . , . 5. . - . - , . _____________________________________________________________________ : 9

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6. ; . . 7. ; . . 1.2 8. ; , = = . , . 9. . -

= = = = = + = = = +

10. : , . , . . 1.3 11. . , . . 1 / / 2 / / 3 = =

1 2 3_____________________________________________________________________ : 10

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1.5 12. ; , . 13. ; , , . . 14. ; , . 1.6 15. ; . 1.4 .

2 2.1 0 v 180 16. ; y = = x = = x 2 + y 2 ( x, y ) = y = = x 17. . 30 45 60 90 0 0 1 01 23 2 3 3

180 0 -1 0

2 22 2

3 21 2

1 0 -

1

3

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2.2 18. 180 ; 180 - (180 ) = - (180 ) = -

(180 ) =

2.3 19. . y x = = .

: - 2 + 2 = 1 = x 2 + y 2 2 = x 2 + y 2 . 2 :

-

x y 2 x2 y 2 y = 2 + 2 1 = + = 2 2 2 + = 1 = y

2

2

=

x

y y = = = = x x x

2.4 20. . .

= =

21. . , . 2 = 2 + 2 2 2 2 2 = + 2 2 2 2 = + 2

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