Chapter 9 Radical Functions

Homework 9.5
SSM: Intermediate Algebra
31.
2 + x = x + 12
( 2 + x ) = ( x + 12)
2 2
4 + 4 x + x = x + 12
35.
x −
2x
= −1
2x
= x + 1
( 2x
) = ( x + 1)
2 2
4 x = 8
2x = x + 2 x + 1
33.
( x )
x = 2
2
2
= 2
x = 4
Check x = 4
?
( ) ( )
2 + 4 = 4 + 12
4 = 4 true
The solution is 4.
x − 1 = 5 − x
( x − 1) = ( 5 − x )
2 2
x − 2 x + 1 = 5 − x
2
2
2x
− 4 = 2
x − 2 =
x
2
( x − 2) = ( x )
x − 4x + 4 = x
x
− 5x
+ 4 = 0
( x )( x )
− 4 − 1 = 0
x
x − 4 = 0 or x − 1 = 0
x = 4 or x = 1
Check x = 4
?
( 4) − 1=
5 − ( 4)
1 = 1 true
Check x = 1
?
( 1) − 1=
5 − ( 1)
0 = 2 false
The solution is 4.
?
2
37.
2
2
x − 1 = 2
( x − 1) 2
= ( 2 x ) 2
x − 2x + 1 = 4x
x
− 6x
+ 1 = 0
x
2
( 6) ( 6) 4( 1)( 1)
2( 1)
− − ± − −
x =
=
6 ± 32
2
= 3 ± 2 2
Check 3+ 2 2 ( x ≈ 5.83)
( ) ( ) ?
5.83 − 2 5.83 =−1
?
− 1.00 =−1 true
Check 3 − 2 2 ( x ≈ 0.172)
( ) ( ) ?
0.172 − 2 0.172 =−1
?
− 0.172=−1 false
The solution is 3 + 2 2 .
x + 1 = − x −7
( x + 1) = ( − x −7)
2 2
x + 1 = x + 14 x + 49
14 x = −48
7 x − 24
( 7 x ) = ( −24)
2 2
49x
= 576
576
x =
49
576
x = x ≈ 11.76
49
Check ( )
?
( ) ( )
11.76 + 1 =− 11.76 − 7
?
3.57 =−10.43 false
There are no real solutions.
292