2056-6h decada
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Transcript of 2056-6h decada
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1
6
51. ) 2 + 2 ) 2 + 2 = + , .
)
2 + 2 = ( + ) ( + ) = ( + )( 1)
)
2 + 2 = + 2 + 2 = 0
(), ( + ) ( 1) = 0 + = 0 1 = 0 = = 1 , ,
52. (x) = x4 4x2 Q(x) = 2x3 x2 8x + 4 ) . ) (x) = Q(x) ) x (x)Q(x) .
) (x) = x4 4x2 = x2( x2 4) = x2 (x2)(x + 2) Q(x) = 2x3 x2 8x + 4 = x2(2x 1) 4(2x1) = = (2x 1)(x2 4) = = (2x 1)(x2)(x + 2) ) (x) = Q(x) x4 4x2 =2x3 x2 8x + 4 () x
2 (x 2)(x + 2) = (2x 1)(x 2)(x + 2)
x2 (x 2)(x + 2) (2x 1)(x 2)(x + 2) = 0
(x 2)(x + 2)[x2 (2x 1)] = 0 (x 2)(x + 2)(x2 2x +1) = 0 (x 2)(x + 2)(x 1)2 = 0 x 2 = 0 x = 2 x + 2 = 0 x = 2 x 1 = 0 x = 1 ) Q(x) 0 (2x 1)(x 2)(x + 2) 0 2x 1 0 x 1
2
x 2 0 x 2
x + 2 0 x 2
(x)Q(x) =
2x (x 2)(x + 2)(2x 1)(x 2)(x + 2)
=
2x
2x 1
-
2
24x
2x + 3
4x + 11
3x-1
6x
53. = {1 , 2 , 3 , 4 , 5} = {1 , 2 , 4} = {2 , 3 , 4 , 5}. .
() , () , () , () , ( ) , ()
() = N(A)( ) = 35
, () = N()( ) = 45
={2 , 4} () = N( )( )
=
25
= {1, 2, 3, 4, 5} () = N( )( )
=
55
= 1
= {3 , 5} = {1} () = N(A )( )
=
25
() = N( )( )
=
15
54 . // , = 6x , AE = 4x + 11 , B= 3x 1, =2x + 3 = 24x ) .
) .
) // , = . = , .
)
=
=
= + = 6x + 3x 1 = 9x 1 = + = 4x + 11 + 2x + 3 = 6x + 14
9x 1
6x
= 6x 144x 11
+
+=
24x
(1)
(1) 9x 16x
= 6x 144x 11
+
+ (9x1)(4x + 11) = 6x(6x + 14)
36x2 + 99x 4x 11 = 36x2 + 84x 11x = 11 x = 1 = 9 1= 8 , = 6 + 14 = 20 , = 6 , = 4 + 11 = 15 , = 24
(1) 9x 16x
=24x
86
= 24
= 18
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3
55.
) 3x 1 y 2 1
5 32x 3 y 1 5
2 3 6
+ + =
+ =
) x = 3 y =1 , (3 + 1)x 2y = 2 (3, 1)
) 3x 1 y 2 1
5 32x 3 y 1 5
2 3 6
+ + =
+ =
3x 1 y 215 15 1 155 3
2x 3 y 1 56 6 62 3 6
+ + =
+ =
3 (3x 1) 5 (y 2) 153 (2x 3) 2 (y 1) 5 + + =
+ =
9x 3 5y 10 156x 9 2y 2 5
+ =
=
9x 5y 226x 2y 16
=
=
9x 5y 223x y 8
=
=
9x 5y 22 1
3x y 8 5 =
=
9x 5y 22
15x 5y 40 =
+ =
6x 18
3x y 8 =
=
x 3
y 1 =
=
) (3 + 1)3 21 = 2 9 + 3 2 = 2
= 38
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56.
= ( 4) + ( )2 3(2 3) 2 = ( 1)2 ( 6 2) 4( 1) 1 ) ) + = 0
) = ( 4) + ( )2 3(2 3) 2 = 2 4 + 2 2 + 2 6 + 9 2 = =
2 4 2 + 2 6 + 9
= ( 1)2 ( 6 2) 4( 1) 1 = 2 2 + 1 2+ 6 + 2 4 + 4 1 = = 2 + 4 ) + = 0 2 4 2 + 2 6 + 9 + 2 + 4 = 0
2 4 + 2 6 + 9 + 4 = 0
(2 4 + 4 ) + (2 6 + 9 ) = 0 ( 2)2 + ( 3)2 = 0 2 = 0 3 = 0 = 2 = 3
57. = , =
// . ) ) E = )
) = , = , = . ( ), . ) E = . ) // , = . E = , = E = , , .
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5
9 11-3 -2 -1 210
95
-10-8 -3 -2 -1 210
58. .
) 4(x + 4) + x + 1 > 2(4x5) 6(x11) 4(x2) 3(x + 1) ) x7 < 1 + 2x 2x6 < 3x + 4 92x 3x18
) 4(x + 4) + x + 1 >2 (4x5) 6(x11) 4(x2) 3(x + 1) 4x + 16 + x + 1> 8x10 6x66 4x8 3x 3 3x > 27 5x 55 x < 9 x 11
x < 9 ) x7 < 1 + 2x 2x6< 3x + 4 92x 3x18 x < 8 x < 10 5x 9
x >8 x >10 x 95
8 < x 95
59. Q(x) = (x 1)3 x( x 2)2 + 3x7 (x) = x(x 2)2( x + 4) x2(x 2)(x + 4)2 ) Q(x) = x2 + 2x 8 ) Q(x) P(x) ) Q(x) = 0 P(x) = 0 ) (x)Q(x) x .
) Q(x) = (x 1)3 x( x 2)2 + 3x7 = x3 3x2 + 3x 1 x( x2 4x + 4) + 3x7 = = x
3 3x2 + 3x 1 x3 + 4x2 4x + 3x7 =
= x2 + 2x 8
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6
) Q(x) = 36 x= 4 x = 2. Q(x) = 1( x + 4)(x 2) = ( x + 4)(x 2) (x) = x(x 2)2(x + 4) x2(x 2)(x + 4)2 = x(x 2)(x + 4) [(x 2) x(x + 4) ] = = x(x 2)(x + 4) (x 2 x2 4x) = = x(x 2)(x + 4) ( x2 3x 2) = = x(x 2)(x + 4) (x2 + 3x + 2) = = x(x 2)(x + 4) (x + 1)(x + 2) ) Q(x) = 0 (x + 4)(x 2) = 0 x + 4 = 0 x 2 = 0 x = 4 x = 2
P(x) = 0 x(x 2)( x + 4) ( x + 1)(x + 2) = 0 x = 0 x 2 = 0 x + 4 = 0 x + 1= 0 x + 2 = 0 x = 0 x = 2 x = 4 x = 1 x = 2
) Q(x) 0 x 4 x 2
(x)Q(x) =
x(x 2)(x + 4)(x + 1 )(x+ 2) (x + 4)(x 2)
= x( x + 1)(x + 2)
60 . 100 . 44 60 , 22 .
) ) . : i) ii) iii)
)
) i . 40 ,
, () = ( )( )
=
40100
= 40%
ii. 44 + 18 = 62 , ,
() = ( )( )
=
62100
= 62%
iii. 16 , ,
() = ( )( )
=
16100
= 16%
44 18 16 22
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