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CHAPTER 5
Study Guide and Review
Continued
Solve each equation.
45.
√
x
-
3
+
5
=
15
46.
-
√
x
-
11
=
3
-
√
x
47.
4
+
√
3
x
-
1
=
8
48.
√
m
+
3
=
√
2
m
+
1
49.
√
2
x
+
3
=
3
50.
(
x
+
1)
1
_
4
= -
3
51.
a
1
_
3
-
4
=
0
52.
3(3
x
-
1)
1
_
3
-
6
=
0
53.
PHYSICS
The formula
t
=
2
π
√
ℓ
_
32
represents the swing
of a pendulum, where
t
is the time in seconds for the
pendulum to swing back and forth and
ℓ
is the length of
the pendulum in feet. Find the length of a pendulum that
makes one swing in 2.75 seconds.
Solve each inequality.
54.
2
+
√
3
x
-
1
<
5
55.
√
3
x
+
13
-
5
≥
5
56.
6
-
√
3
x
+
5
≤
3
57.
√
-
3
x
+
4
-
5
≥
3
58.
5
+
√
2
y
-
7
<
5
59.
3
+
√
2
x
-
3
≥
3
60.
√
3
x
+
1
-
√
6
+
x
>
0
Example 6
Solve
√
2
x
+
9
-
2
=
5.
√
2
x
+
9
-
2
=
5
Original equation
√
2
x
+
9
=
7
Add 2 to each side.
(
√
2
x
+
9
)
2
=
7
2
Square each side.
2
x
+
9
=
49
Evaluate the squares.
2
x
=
40
Subtract 9 from each side.
x
=
20
Divide each side by 2.
Example 7
Solve
√
2
x
-
5
+
2
>
5.
√
2
x
-
5
≥
0
Radicand must be
≥
0.
2
x
-
5
≥
0
Square each side.
2
x
≥
5
Add 5 to each side.
x
≥
2.5
Divide each side by 2.
The solution must be greater than or equal to 2.5 to satisfy
the domain restriction.
√
2
x
-
5
+
2
>
5
Original inequality
√
2
x
-
5
>
3
Subtract 2 from each side.
(
√
2
x
-
5
)
2
>
3
2
Square each side.
2
x
-
5
>
9
Evaluate the squares.
2
x
>
14
Add 5 to each side.
x
>
7
Divide each side by 2.
Because
x
≥
2.5 contains
x
>
7, the solution of the inequality
is
x
>
7.
5-6
Solving Radical Equations
364
|
Chapter 5
|
Study Guide and Review