Chapter 9 Radical Functions

SSM: Intermediate Algebra Homework 9.2
2
45. ( )( ) ( ) 2
1− x 1+ x = 1 − x = 1−
x
2 2
x + 5 x − 5 = x − 5 = x − 25
47. ( )( ) ( ) ( )
2 2
2
49. ( 5 + 6 x ) = 5 + 2( 5)( 6 x ) + ( 6 x )
2
2
= 25 + 60 x + 6 ( x )
= 25 + 60 x + 36x
= 36x
+ 60 x + 25
2 2 2
51. ( 7 x − 1) = ( 7 x ) − 2( 7 x )( 1) + ( 1)
2
( x )
2
= 7 − 14 x + 1
= 49x
− 14 x + 1
2 2 2
53. ( 4 x + 5) = ( 4 x ) + 2( 4 x )( 5) + ( 5)
2
( x )
2
= 4 + 40 x + 25
= 16x
+ 40 x + 25
2 2 2
55. ( x + 1) = ( x ) + 2( x )( 1) + ( 1)
57.
= x + 2 x + 1
1 1
+
5 1/ 2 1/ 5 2 5
x x = x ⋅ x = x
5 2
+
10 10
= x = x
=
10 7
x
7 /10
59. 5 4 5 3 5 4 3 5 7
x x = x ⋅ x = x
5 5 2 5 5 5 2
= x ⋅ x = x x
= x
5 2
x
61. −5 x ( 4 2x − 4) = −5 x 4 2x − 5 x ( −4)
4 4
5 2 20
= − x x + x
4 1/ 2 1/ 4
5 2 20
= − x ⋅ x + x
1 1
+
4 2 4
= − 5 2 x + 20
4 3/ 4
5 2 20
= − x +
4 4 3
5 2 20
= − x +
4 3
= − 5 2x
+ 20
3 3 3
63. ( x + 1) = ( x ) + 2( x )( 1) + ( 1)
x
x
x
2 2 2
3 2 3
= x + 2 x + 1
2 2 2
3 3 3
65. ( x − 2) = ( x ) − 2( x )( 2) + ( 2)
3 2 3
= x − 4 x + 4
2 2 2
4 3 4 4 3 3
67. ( x + x ) = ( x ) + 2( x )( x ) + ( x )
69. ( 2 x − 6)( 3 3 x + 1)
4 2 1/ 4 1/ 3 3 2
= x + 2x ⋅ x + x
1 1
+
2 / 4 4 3 3 2
= x + 2x + x
1/ 2 7 /12 3 2
= x + 2x + x
12 7 3 2
= x + 2 x + x
3 3
2 3 6 3 2 1 6 1
= x ⋅ x − ⋅ x + x ⋅ − ⋅
1/ 2 1/ 3 3
= 6x ⋅ x − 18 x + 2 x − 6
1 1
+
2 3 3
6 18 2 6
= x − x + x −
5/ 6 3
= 6x − 18 x + 2 x − 6
6 5 3
= 6 x − 18 x + 2 x − 6
6 5 3
= 6 x + 2 x −18 x − 6
x
4 4 4
71. ( 3 x + 5)( 3 x − 5) = ( 3 x ) − ( 5)
( x )
2 4
2 2
= 3 − 25
2
= 9 x − 25
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