Chapter 9 Radical Functions

SSM: Intermediate Algebra Homework 9.5
39.
x − 3 + x + 5 = 4
43.
2x
− 1 + 3x
− 2 = 2
x − 3 = 4 − x + 5
( x − 3) = ( 4 − x + 5)
2 2
2x
− 1 = 2 − 3x
− 2
( 2x
− 1) = ( 2 − 3x
− 2)
2 2
x − 3 = 16 − 8 x + 5 + x + 5
2x − 1 = 4 − 4 3x − 2 + 3x
− 2
8 x + 5 = 24
4 3x
− 2 = x + 3
41.
x + 5 = 3
( ) 2 2
x + 5 = 3
Check x = 4
x + 5 = 9
( ) ( )
x = 4
4 − 3 + 4 + 5 = 4
4 = 4 true
The solution is 4.
x − 4 = x + 6 + 2
( x − 4) = ( x + 6 + 2)
( x 6)
2 2
x − 4 = x + 6 + 4 x + 6 + 4
4 x + 6 = −14
7
x + 6 = −
2
2
2 ⎛ 7 ⎞
+ = ⎜ − ⎟
⎝ 2 ⎠
49
x + 6 =
4
25
x =
4
25
Check x =
4
25
?
25
⎛ ⎞ ⎛ ⎞
⎜ ⎟ − 4 = ⎜ ⎟ + 6 + 2
⎝ 4 ⎠ ⎝ 4 ⎠
?
3
?
11
= false
2 2
There are no real solutions.
45.
47.
( 4 3x
− 2) = ( x + 3)
x
2
( )
( x )( x )
2 2
16 3x − 2 = x + 6x
+ 9
48x − 32 = x + 6x
+ 9
− 42x
+ 41 = 0
− 41 − 1 = 0
x − 41 = 0 or x − 1 = 0
x = 41 or x = 1
Check x = 41
( ) ( )
2 41 − 1 + 3 41 − 2 = 2
( ) ( )
2 1 − 1 + 3 1 − 2 = 2
2
2
?
?
20=
2 false
2 = 2 true
The solution is 1.
x − 2 = 3
( x )
2
( x )
2
2
− 2 = 3
x − 2 = 9
x = 11
2
= 11
x = 121
Check x = 121
( )
?
121 − 2 = 3
3 = 3 true
The solution is 121.
1
+ x = 2
x
⎛ 1 ⎞
x ⋅ ⎜ + x ⎟ = x ⋅2
⎝ x ⎠
?
293