Chapter 9 Radical Functions

SSM: Intermediate Algebra Homework 9.5
21.
−4.91 3.18x
− 7.14 = −2.19
2.19
3.18x
− 7.14 =
4.91
( 3.18x
7.14 )
2 ⎛ 2.19 ⎞
− = ⎜ ⎟
⎝ 4.91 ⎠
⎛ 2.19 ⎞
3.18x
− 7.14 = ⎜ ⎟
⎝ 4.91 ⎠
Check x = 2.3078
⎛ 2.19 ⎞
3.18x
= 7.14 + ⎜ ⎟
⎝ 4.91 ⎠
( )
⎛ 2.19 ⎞
7.14 + ⎜ ⎟
4.91
x =
⎝ ⎠
3.18
x = 2.3078
−4.91 3.18 2.3078 − 7.14 =− 2.19
− 2.19 = −21.19 true
The solution is approximately 2.3078.
?
2
2
2
2
2
12x + 13 = 9x − 12x
+ 4
9x
− 24x
− 9 = 0
2
( x x )
3 3 − 8 − 3 = 0
( x )( x )
3 3 + 1 − 3 = 0
3x
+ 1 = 0 or x − 3 = 0
1
x = − or x = 3
3
1
Check x = −
3
1
?
1
⎛ ⎞ ⎛ ⎞
12⎜ − ⎟ + 13 + 2 = 3⎜ − ⎟
⎝ 3 ⎠ ⎝ 3 ⎠
Check x = 3
?
2
5=−1 false
( ) + + = ( )
12 3 13 2 3 3
9 = 9 true
The solution is 3.
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23.
25.
x
( 3x
+ 3) = ( x − 5)
2
3x
+ 3 = x −5
( x )( x )
2 2
2
3x + 3 = x − 10x
+ 25
− 13x
+ 22 = 0
−11 − 2 = 0
x − 11 = 0 or x − 2 = 0
x = 11 or x = 2
Check x = 11
?
( ) ( )
3 11 + 3 = 11 − 5
6 = 6 true
Check x = 2
?
( ) ( )
3 2 + 3= 2 − 5
3=−
3 false
The solution is 11.
?
12x
+ 13 + 2 = 3x
12x
+ 13 = 3x
− 2
( 12x
+ 13) = ( 3x
− 2)
2 2
27.
29.
3x
+ 4 − x = 3
( 3x
+ 4) = ( x + 3)
x
2
3x
+ 4 = x + 3
2 2
3x + 4 = x + 6x
+ 9
+ 3x
+ 5 = 0
2
2
( ) − ( )( )
2( 1)
− 3 ± 3 4 1 5
x =
− 3 ± −11
=
2
There are no real solutions.
2
x − 5x + 1 = x − 3
2
2
( x − 5x + 1) = ( x − 3)
2 2
x − 5x + 1 = x − 6x
+ 9
Check x = 8
x = 8
?
2
( ) ( ) ( )
8 − 5 8 + 1 = 8 − 3
5 = 5 true
The solution is 8.
2
291