Επανάληψη Γυμνασίου(1)

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Επανάληψη Γυμνασίου

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    17. ,

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  • 32 = 3 3 = 9 , 8 7 7 > 3, > () !! 14 = 1 1 1 1 = 1 , 8 4 1, > () !!>, 8, 1 7 > ( 8 7 C C ( | | .

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    20. .

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    8 = 4 2 = 22 2 = 2 2 .

    12 = 4 3 = 22 3 = 2 3 .

    18 = 9 2 = 32 2 = 3 2 .

    75 = 25 3 = 52 3 = 5 3 .

    300 = 100 3 = 102 3 = 10 3 .

    + = + !!! (1 ' 7 !!).

    = !!! (1 ' 7 !!).

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    x +y + 2x + 2y = (x +y)+ (2x + 2y) = (x +y)+ 2(x +y) = (x +y)(+ 2) . .

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    2.

    3x312x 2 + 5x 20 = (3x 312x 2)+ (5x 20) = 3x 2(x 4)+ 5(x 4) = (x 4)(3x 2 + 5) .

    3.

    33 + 9 = (3)+ (3 + 9) = (3)3(3) = (3)(3) . .

    33 + 9 = (3)+ (3+ 9) = (3)3(3) = (3)(3) .

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  • 9x2 12x + 4 = (3x)2 2 3x 2 + 22 = (3x 2)2 .

    x21 = x 212 = (x +1)(x 1) ( !)

    1x2 = 12x 2 = (1+ x)(1x) ( !)

    x2 4 = x 222 = (x + 2)(x 2) ( !)

    4x2 = 22x 2 = (2 + x)(2x) ( !)

    x29 = x 232 = (x + 3)(x 3) ( !)

    9x2 = 32x 2 = (3 + x)(3x) ( !)

    x216 = x 2 42 = (x + 4)(x 4) ( !)

    16x2 = 42x 2 = (4 + x)(4x) ( !)

    4x225 = (2x)252 = (2x + 5)(2x 5) .

    169x2 = 42(3x)2 = (4 + 3x)(43x) .

    x3 +1 = x 3 +13 = (x +1)(x 2 x 1+12) = (x +1)(x 2 x +1) ( !)

    x3 1 = x 3 13 = (x 1)(x 2 + x 1+12) = (x 1)(x 2 + x +1) ( !)

    1x3 = 13 x 3 = (1x)(12 +1 x + x 2) = (1x)(1+ x + x 2) ( !)

    x3 + 8 = x 3 + 23 = (x + 2)(x 2 x 1+ 22) = (x + 2)(x 2 2x + 4) ( !)

    x3 8 = x 3 23 = (x 2)(x 2 + x 2 + 22) = (x 2)(x 2 + 2x + 4) ( !)

    8x3 = 23 x 3 = (2x)(22 + 2 x + x 2) = (2x)(4 + 2x + x 2) ( !)

    4 . .

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  • x2 + x + = (x x

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    ( > ( (- 7 > 7, ( > ' (, 7).

    (: L = 2

    L2

    =22 =

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    .

    2. 1 1 P = 2x + 2y y (( y 7 > 7).

    (: P = 2x + 2y P 2x = 2y

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    .

    3. 1 1 =

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    (

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    2 2 = ( +) 2 = + 2 =

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    .

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    27. .

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    32. ( )

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    33. .

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  • 7 C 8 ( , 8 ( 7 >!

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    7, C C (8 1) >, , 1 1, > 7 ( x =3 .

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    35.

    .

    !!!

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