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  1. Top | #1

    Apr 2012
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  2. Top | #2

    Apr 2012
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    :

    ^2 + ^2 + 3 + 3 = 8
    + 4 + 4 = 2




    + 4 + 4 = 2

    = 2 - 4*( + ) (1)

    ^2 + ^2 + 3 + 3 = 8

    [( + )^2 - 2 ] + 3*( + ) = 8
    ( + )^2 + 3*( + ) = 8 + 2 (2)

    (1) (2)

    ( + )^2 + 11*( + ) - 12 = 0

    ( + ) =

    ^2 + 11 - 12 = 0
    ( - 1)( + 12) = 0

    = 1
    + = 1
    = 2 - 4*1 = - 2 = - 2/
    - 2/ + - 1 = 0
    1/*(^2 - - 2) = 0

    1/ = 0

    ^2 - - 2 = 0
    = 2 = - 1
    = - 1 = 2




    = - 12
    + = - 12
    = 2 - 4*(- 12) = 50 = 50/
    50/ + + 12 = 0
    1/* ( ^2 + 12 + 50 ) = 0

    ^2 + 12 + 50 = 50
    = [- 12 + - (144 - 4*1*50) / 2
    = [-12 + - - 56]/2

    = - 6 + 14 () = 7 - 14
    = - 6 - 14 () = 7 + 14

  3. Top | #3

    Apr 2012
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    ( ) = ^4 - 2 ^3 + 4 ^2 + +




    () ( - 1)( - 1) : = 0

    :

    = ^2 + 3

    = ( + 6 ) + ( - 3) = 0
    :
    = - 6
    = 3

    :

    ( - )( - ) = ^2 + 3

    ^2 - ( + ) + = ^2 + 3

    + = 0 = -
    = 3



    - ^2 = 3 = 3
    = - 3

  4. Top | #4

    Apr 2012
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    + 2 - 2 = - 1 ... ... ... ... ... (1)

    2 + - = 1 ... ... ... ... ... .... (2)

    3 - 2 + 4 = 11 ... ... ... ... ... (3)



    (1) (3) 2 = 5 -

    (2) 2 - = 4

    (3)
    = 1
    = 2
    = 3


    :

    (1) ( - ) = - (1 + )/2

    (2)
    2 + ( - ) = 1 = 1

    - = - 1 = + 1

    (3)
    3*1 - 2* + 4*( + 1) = 11
    3 + 2 + 4 = 11 = 2
    = 3



    = + = +



    | - |^2 + | + |^2 = 2 ( | |^2 + | |^2 )



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

    - = ( + ) + (- - ) = ( - ) + *( - )
    + = ( + ) + ( + ) = ( + ) + *( + )

    [ - ] = [( - )^2 + ( - )^2]
    [ + ] = [( + )^2 + ( + )^2]

    | - |^2 + | + |^2 = [( - )^2 + ( - )^2] + [( + )^2 + ( + )^2]

    = 2*(^2 + ^2) + 2*(^2 + ^2) = 2*( | |^2 + | |^2 )


























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    3

    2 ( +3)^3 + 4( +3) - 5 = 0



















































































































    - /





































    ^2 = 12 ^2 = 6 ^2 = 18


    (1 )

    ( 2) + +




    ^2 = 12 ... ... ... (1)

    ^2 = 6 ... ... ... .(2)

    ^2 = 18 ... ... ... (3)

    (1) (2) ... ... / = 2

    (2) (3) ... ... / = 3

    (1) (3) ... ... / = 3/2

    (1)

    ^2 * /2 * 3 /2 = 3/4 * ^4 = 12

    ^4 = 4 * 12 / 3 = 16

    = + - 2

    (2)

    = + - 1

    (3)

    = + - 3

    :

    ( 2 1 3 ) ( - 2 - 1 - 3 )

    * * = 6 - 6

    + + = 6 - 6

    :

    [ (+1)/(-1)]^3 -3 [ (+1)/(-1)]^2 +[ (+1)/(-1)]+1 = 0




    [( + 1)/( - 1)] =

    ^3 - 3 ^2 + + 1 = 0

    ( - 1)(^2 - 2 - 1) = 0

    = 1
    ( + 1)/( - 1) = 1 ... ...

    (^2 - 2 + 1) = 0
    = 1 + 2 ... = 1 - 2

    ( + 1)/( - 1) = 1 + 2
    + 1 = (1 + 2)* - 1 - 2
    = 2 + 1

    ( + 1)/( - 1) = 1 - 2
    + 1 = (1 - 2)* - 1 + 2
    = 2 - 1

    = + = ω + ω2 = ω2+ ω
    1 ω ω2
    : = 3 + 3





    :

    ( + 1 ) ( /10 ) = 3



    ( + 1) ( - 1) = 3

    ( )^2 - 1 = 3

    ( )^2 = 4

    = + 2 > = 100

    = - 2 > = 1/100

    :
    ^2 + + = 0 =/= 0

    :
    ^2 - ( ) + = 0



    ^2 + + = 0



    ^2 + (/)* + (/) = 0 ..................(1)

    :

    ( _ )*( - ) = 0

    ^2 - * - * + * = 0

    ^2 - ( + )* + * = 0 ...................(2)

    (1) (2)

    / = - ( + ) = - ( )

    / = * =

    :

    ^2 - ( )* + ( ) = 0

    119 8


    =

    ^2 - 119 = 10( - 8) = 10 - 80

    ^2 - 10 - 39 = 0
    ( - 13)( + 3) = 0

    = 13 = - 3



    2106


    :
    =
    =

    = 5
    ^2 + ^2 = 2106

    26 ^2 = 2106
    ^2 = 81

    = 9
    = 45

    ( 15 56 )



    :

    15/56 = (8 + 7) (8 7) = 1/7 1/8
    : 7 8

    15/56 = [15 *(8 - 7)] [8 7] = 15/7 - 15/8
    : 7/15 - 8/15


    :

    :

    - = 1 ........... : = 1 +

    1/ + 1/ = 15/56

    ( + )/* = 15/56

    (1 + 2 ) 56 = ( + ^2) 15

    15 ^2 - 97 - 56 = 0



    = 7 ............. : = 8



    = - 8/15 ........ : = 7/15

    17 ɿ


    =

    + 17 = 60 /

    ^2 + 17 - 60 = 0
    ( - 3)( + 20) = 0

    = 3 = - 20




    :

    :

    ^2 - ( )* + ( ) = 0

    ^2 + 17 - 60 = 0

    ^2 - (- 17)* + (- 60) = 0

    - 17 = - 20 + 3
    - 60 = - 20 3

    = 3 = - 20

    9 81


    :

    + = 9 ( - )
    ^2 - ^2 = 81

    ( - )( + ) = 81
    9 ( - )^2 = 81
    ( - )^2 = 9
    ( - ) = + 3 - 3

    ( - ) = 3
    : ( + ) = 27
    :
    = 15 = 12

    ( - ) = - 3
    : ( + ) = - 27
    :
    = - 15 = - 12




    =

    + ^2 = 9 ( + 1)
    ^2 - 8 - 9 = 0

    ^2 - [(9 + (- 1)]* + (9 - 1) = 0

    = 9 = - 1











    :
    (+1) 3 + (+4) 3 = 1 + 7 3
    (2-1) 9 + (-2) 9 = 1/2


    (+1) 3 + (+4) 3 = 1 + 7 3
    [( + 1)( + 4)] 3 = [3 7] 3
    :
    ( + 1)( + 4) = 21 ........................... (1)

    (2-1) 9 + (-2) 9 = 1/2
    [(2 - 1)( - 2)] 9 = 1/2 = [9^1/2] 9
    :
    (2 - 1)( - 2) = 9^1/2 = 3 ................... (2)

    (1) (2)
    :
    = 6
    = 6/ (2)
    4 ^2 - 11 + 6 = 0

    :
    = 2 > = 3

    = 3/4 > = 8

    41

    :
    :
    + = 1 > ( + )^2 = 1
    ^2 + ^2 + 2 = 1
    :
    ^2 + ^2 = 41
    :
    41 + 2 = 1 > = - 20
    = 1 -
    ( 1 - ) = - 20
    ^2 - - 20 = 0
    ( - 5 ) ( + 4 ) = 0
    = 5 > = - 4

    = - 4 > = 5

    : - 4 5

    1 16





    1 16 : 8 16

    8 1

    16 9

















































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  5. Top | #5

    Apr 2012
    14804
    -
    0.14
    598
    Thanked: 119

    -













































    3 ^4 - 5 ^2 - 2 =




    (3^2 + 1)(^2 - 2) = 0

    (3^2 + 1) = 0 ... ... ... = + - /3

    (^2 - 2) = 0 ... ... ... = + - 2

    ( )



    ( ) = ( + 1 ) ^3 - 2 ^2 +

    ( - 2 ) 9




    :

    ( + 1 ) ^3 - 2 ^2 + - 9 + 9 =

    ( + 1 ) ^3 - 2 ^2 - 8 + 9 =

    ( - 2 )*[ ( + 1) ^2 + 2 + 4 ] + 9

    ( - 2 ) = 9

    = 1



    [( + 1 ) ^3 - 2 ^2 + ]/( - 2) =

    [ 2^3 - 2^2 + 1]/( -2) = 2*( - 1)( + 2) + 9/( - 2)

    - : ^2 +/- * + ^2 >/= 0


    ( + )^2 = ^2 + ^2 + 2 *
    * = 1/2*[( + )^2 - (^2 + ^2)]

    ( - )^2 = ^2 + ^2 - 2 *
    - * = 1/2*[( - )^2 - (^2 + ^2)]

    :

    ^2 + * + ^2 = ^2 + 1/2*[( + )^2 - (^2 + ^2)] + ^2
    = 1/2*[( + )^2 + (^2 + ^2)] > 0

    ^2 - * + ^2 = ^2 + 1/2*[( - )^2 - (^2 + ^2)] + ^2
    = 1/2*[( - )^2 + (^2 + ^2)] > 0

    = = 0

































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