Chapter 9 Radical Functions

Chapter 9 Review Exercises
SSM: Intermediate Algebra
37.
38.
( 4x
5)
x
2
4x
+ 5 = x
2
+ = x
4x
+ 5 = x
− 4x
− 5 = 0
( x )( x )
− 5 + 1 = 0
x − 5 = 0 or x + 1 = 0
x = 5 or x = −1
Check x = 5
?
( ) + = ( )
4 5 5 5
5 = 5 true
Check x = − 1
2
2
( − ) + = ( − )
4 1 5 1
1=−1 false
The solution is 5.
?
?
2x
− 4 = x − 2
( 2x
− 4) = ( x − 2)
2 2
40.
Check x = 9
?
( 9) + 6=
( 9)
9 = 9 true
Check x = 4
?
( 4) + 6 = ( 4)
8=
4 false
The solution is 9.
?
13x
+ 4 = 5x
− 20
( 13x
+ 4) = ( 5x
− 20)
2 2
13x
+ 4 = 5x
− 20
8x
= −24
x = −3
Check x = − 3
?
( ) ( )
13 − 3 + 4 = 5 −3 − 20
?
− 35 = −35
There is no real solution.
39.
x
2
( x )( x )
2x − 4 = x − 4x
+ 4
− 6x
+ 8 = 0
− 4 − 2 = 0
x − 4 = 0 or x − 2 = 0
x = 4 or x = 2
Check x = 4
?
( ) ( )
2 4 − 4 = 4 − 2
2 = 2 true
Check x = 2
?
( ) ( )
2 2 − 4 = 2 − 2
0 = 0 true
The solutions are 4 and 2.
x
2
x + 6 = x
2
( x ) = ( x − 6)
( x )( x )
x = x − 6
− 13x
+ 36 = 0
− 9 − 4 = 0
2 2
2
x = x − 12x
+ 36
x − 9 = 0 or x − 4 = 0
x = 9 or x = 4
41.
x
2x
− 1 = 1+ x + 3
( 2x
− 1) = ( 1+ x + 3)
2 2
2x − 1 = 1+ 2 x + 3 + x + 3
2 x + 3 = x −5
( 2 x + 3) = ( x − 5)
2
( )
( x )( x )
2 2
4 x + 3 = x − 10x
+ 25
2
2
4x + 12 = x − 10x
+ 25
− 14x
+ 13 = 0
−13 − 1 = 0
x − 13 = 0 or x − 1 = 0
x = 13 or x = 1
Check x = 13
?
( ) ( )
2 13 − 1 = 1+ 13 + 3
5 = 5 true
Check x = 1
?
( ) ( )
2 1 − 1= 1+ 1 + 3
1=
3 false
The solution is 13.
?
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