Chapter 9 Radical Functions

Homework 9.5
SSM: Intermediate Algebra
49.
2
1+ x = 2
2
( 1+ x) = ( 2 x )
1+ 2x + x = 4x
x
2
− 2x
+ 1 = 0
( x )( x )
−1 − 1 = 0
x − 1 = 0
x = 1
Check x = 1
1
+ ( 1) =
?
2
1
( )
2 = 2 true
The solution is 1.
1
= 3 − x + 2
x + 2
1
x + 2 ⋅ = x + 2 3 − x + 2
x + 2
x
( 3 x + 2) = ( x + 3)
x
2
( )
2 2
2
2
2
( )
1 = 3 x + 2 − x − 2
3 x + 2 = x + 3
9 x + 2 = x + 6x
+ 9
9x + 18 = x + 6x
+ 9
− 3x
− 9 = 0
( 3) (
2
3) 4( 1)( 9)
2( 1)
− − ± − − −
x =
3 ± 3 5
=
2
3 + 3 5
2
1
?
= 3 − ( 4.85)
+ 2
4.85 + 2
Check ( x ≈ 4.85)
( )
0.382 = 0.382 true
3 − 3 5
2
1
?
= 3 − ( − 1.8541)
+ 2
− 1.8541 + 2
Check ( x ≈ − 1.8541)
( )
2.62 = 2.62 true
The solutions are 3 ± 3 5
2
.
51.
53.
3 x + 4 − 7 x + 1
3 x − 7 x + 4 + 1
( 3 − 7) x + ( 4 + 1)
− 4 x + 5
3 x + 4 − 7 x + 1= −7
Check x = 9
− 4 x + 5 = −7
− 4 x = −12
x = 3
( ) 2 2
x = 3
( ) ( )
x = 9
3 9 + 4 − 7 9 + 1=−
7
− 7 =− 7 true
The solution is 9.
55. ( x )( x )
?
?
+ 3 + 1 = 3
x ⋅ x + 3⋅ x + x ⋅ 1+ 3⋅ 1 = 3
Check x = 0
( ( ) ) ( )
x + 3 x + x + 3 = 3
x + 4 x = 0
( 4 x ) = ( −x)
x
2
( ) ?
0 + 3 0 + 1 = 3
Check x = 16
( ( ) ) ( )
4
( )
x = −x
2 2
16x
= x
− 16x
= 0
x x − 16 = 0
x = 0 or x − 16 = 0
x = 0 or x = 16
3 = 3 true
( ) ?
16 + 3 16 + 1 = 3
The solution is 0.
?
35=
3 false
2
294