Γ Γυμνασίου παράγρ 1.2 -1.5 σχ. έτος 2014 15

download Γ Γυμνασίου παράγρ 1.2 -1.5 σχ. έτος 2014 15

of 17

  • date post

    30-Jul-2015
  • Category

    Education

  • view

    8.951
  • download

    0

Embed Size (px)

Transcript of Γ Γυμνασίου παράγρ 1.2 -1.5 σχ. έτος 2014 15

1. - 2014-20151 : 2. 1. ; ; ; ... 65+28 252+58 , , ... 2x2 + , ..2x2 + xy , . , 2x2 + xy x = 5 y =8, 252 + 58 = 90.2. ; ; ; , , ... 4 , 32 . , .. 32 3 .2 : 3. 2 . , .. 32 :2 1 3 .3. ; ; ; ; ; .. , , . 2x3y -2x3y . ., 0 , , 5 .3 : 4. 1. ; ; ; ; ; ; , , ... 32+24-533 ... 32+24-533 3 32,24,-533 ., , . 32+24-533 :3 4 6 ., , , ., , .2. ; -3x + 2x2 + 5 x P(x) Q(x) A(x) ... P(x) = -3x + 2x2 + 5 , .4- , - , . : 5. , P(x) = 2x2 - 3x + 5., , x.H P(x) x = 5, P(5) :P(5) = 252- 35 + 5 = 50 - 15 + 5 = 40.3. , . 3x2 - 5x + 1 x2 + x + 1 , = 3 = -5. , , . . , , 4. ; . , A(x) = 3x3 - 2x2 - 7x - 5 B(x) = 2x3 - x2 + x :A(x)+B(x) = (3x3 - 2x2 - 7x - 5) + (2x3 - x2 + x) =( )= 3x3 - 2x2 - 7x - 5 + 2x3 - x2 + x =( )5x3 - 3x2 - 6x - 5., A(x)-B(x)==(3x3 - 2x2 - 7x - 5) - (2x3 - x2 + x) == 3x3 - 2x2 - 7x - 5 - 2x3 + x2 - x == x3 - x2 - 8x - 5.5 ; : 6. 1. ; , .3x2(2x3 + 6x) = 3x22x3 + 3x26x = 6x5 + 18x3 , . , .6 : 7. 1. ; . , ' . :) ( + )( - ) = 2 - 27 ;) ( + )2 = 2 + 2 + 2) ( - )2 = 2 - 2 + 2) ( + )3 = 3 + 32 + 32 + 3) ( - )3 = 3 - 32 + 32 - 3) 3 + 3 = ( + )(2 - + 2)) 3 - 3 = ( - )(2 + + 2) : 8. 2. ;) ( + )2 = 2 + 2 + 2 ( + )2 ( + )( + ) , :( + )2 = ( + )( + ) == 2 + + + 2 == 2 + 2 + 2) ( - )2 = 2 - 2 + 2 ( - )2 ( - )( - ) , :( - )2 = ( - )( - ) = 2 - - + 2 = 2 - 2 + 2) ( + )3 = 3 + 32 + 32 + 3 ( + )3 ( + )( + )2 + ( + )2, :( + )3 = ( + )( + )2 == ( + )(2 + 2 + 2) == 3 + 22 + 2 + 2 + 22 + 3 == 3 + 32 + 32 + 3) ( - )3 = 3 - 32 + 32 - 3 ( - )3 ( - )( - )2 - ( - )2, :( - )3 = ( - )( - )2 == ( - )(2 - 2 + 2) == 3 - 22 + 2 - 2 + 22 - 3 == 3 - 32 + 32 - 38 : 9. ) ( + )( - ) = 2 - 2( + )( - ) = -++ =) 3 + 3 = ( + )(2 - + 2)( + )(2 - + 2)= 2- + 2 + 2- + 2==3 2 + 2 + 2 - 2 + 3 ==3 + 3) 3 - 3 = ( - )(2 + + 2)( - )(2 + + 2)= 2+ + 2 - 2 - - 2==3 + 2 + 2 - 2 - 2 - 3 ==3 - 33. ; : 1 = . 2 = . = = = .9= 2 - - + - 2 == 2 - 2 = , : 10. 4. : (+)2=2+2+210 : 11. 2. . t sec , , 111. : : 12. 3. , , . . ; V 1 = 2. , V2 = (2)2 = (42) = 42. V2 - V1 = 42 - 2 = 32, 2 . .4. P(x) = 4x2 - 8x + x3 - 5 x .) P(x) Q(x) = x2 + x + , , , , ;) P(x) = 4x2 - 8x + x3 - 5, x P(x) = x3 + 4x2 - 8x - 5.To P(x) , 0 , = 0.) P(x) = x3 + 4x2 - 8x - 5 Q(x) = x2 + x + , = 0, = 4, = -8 = -5.5. x 500 , 10 (, , ) 12 : 2 (, ). x ; , 50 ; 13. 10 , x 10x . , 6. P(x) = x2 - 3x + 4, Q(x) = P(2x) , P(x) , x 2x, :P(2x) = (2x)2 - 3(2x) + 4 = 4x2 - 6x + 4 P(-x) , P(x) , x -x, :(-x) = (-x)2 - 3(-x) + 4 = x2 + 3x + 4. :Q(x) = P(2x) - P(-x) = (4x2 - 6x + 4) - (x2 + 3x + 4) =13P(2x) - P(-x).= 4x2- 6x + 4 - x2 - 3x - 4 Q(x) =3x2 - 9x7. : 14. 8. , . , , .H 2x + y 4x + 10, (2x + y)(4x + 10). y x + 10, y(x + 10)., :(2x + y)(4x + 10) - y(x + 10) = = 8x2 + 20x + 4xy + 10y - xy - 10y =8x2 + 20x+ 3xy( + + )2 = 2 + 2 + 2 + 2 + 2 + 2.) (3x + 2y + 4)2.) ( + + )2 = ( + + )( + + ) == 2 + + + + 2 + + + + 2 == 2 + 2 + 2 + 2 + 2 + 2.149. ) : 15. ) , (3x + 2y + 4)2 :(3x + 2y + 4)2 == (3x)2 + (2y)2 + 42 + 23x2y + 22y4 + 23x4 == 9x2+ 4y2 + 16 + 12xy + 16y + 24x.10. : ) 2 + 2 = ( + )2 - 2 ) 3 + 3 = ( + )3 - 3( + ). :) ( + )2 - 2 = 2 + 2 + 2 - 2 = 2 + 2) ( + )3 - 3( + ) = 3 + 32 + 32 + 3 - 32 - 32 = 3 + 3.=3 2+ 1511. + : 3+ 12. , , ; 2. , - + , ( - )( + ) = 2 - 2. , 2 2 -2, 2. 16. 13. 16 : .14. ) ( - 1)( + 1) + 1 = 2. ) 20072009 + 1 , .) ( - 1)( + 1) + 1 = (2 -12) + 1 = 2 - 1 + 1 = 2.) = 2008, - 1 = 2007 + 1 = 2009. :20072009 + 1 = ( - 1)( + 1) + 1 = 2 = 20082., 20072009 + 1 2008.: ..99101 = (100 - 1)(100 + 1) = 1002 - 12 = 10000 - 1 = 99991032 = (100 + 3)2 = 1002 + 21003 + 32 = 1060915. : ) (2x - 3)2 - 2(3x - 1)(3x + 1)) (x - 2y)3 - (x - y)(x2 + xy + y2).) (2x - 3)2 - 2(3x - 1)(3x + 1) == [(2x)2 - 22x3 + 32] - 2[(3x)2 - 12] = 17. = [x3 - 3x22y + 3x(2y)2 - (2y)3] - (x3 - y3) == x3 - 6x2y + 12xy2 - 8y3 - x3 + y3 == -6x2y + 12xy2 - 7y3(2 + 2)(x2 + y2) = (x + y)2 + (y - x)2( Lagrange). 1 :(2 + 2)(x2 + y2) = 2x2 + 2y2 + 2x2 + 2y2 2 :(x + y)2 + (y - x)2 = (x)2 + 2(x)(y) + (y)2 + (y)2 - 2(y)(x) +(x)2 == 2x2 + 2xy + 2y2 + 2y2 - 2xy + 2x2 == 2x2 + 2y2 + 2x2 + 2y2 (2 + 2)(x2 + y2) = (x + y)2 + (y - x)2.17= (4x2 - 12x + 9) - 2(9x2 - 1) == 4x2 - 12x + 9 - 18x2 + 2 == -14x2 - 12x + 11) (x - 2y)3 - (x - y)(x2 + xy + y2)=16. :