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EXTEND 6
Graphing Technology Lab
Solving Radical Equations
Continued
Use a graphical method to solve each equation or inequality.
1.
√
x
+
4
=
3
2.
√
3
x
-
5
=
1
3.
√
x
+
5
=
√
3
x
+
4
4.
√
x
+
3
+
√
x
-
2
=
4
5.
√
3
x
-
7
=
√
2
x
-
2
-
1
6.
√
x
+
8
-
1
=
√
x
+
2
7.
√
x
-
3
≥
2
8.
√
x
+
3
>
2
√
x
9.
√
x
+
√
x
-
1
<
4
10.
WRITING INMATH
Explain how you could apply the technique in the first example to
solving an inequality.
Example 2
Radical Inequality
Solve 2
√
x
>
√
x
+
2
+
1.
Step 1
Graph each side of the inequality and
use the
TRACE
feature.
• In the
Y=
list, enter
y
1
=
2
√
x
and
y
2
=
√
x
+
2
+
1. Then press
.
C07-033A-888482
[ 10, 10 ] scl: 1 by [ 10, 10] scl: 1
• Press
. You can use or to switch the
cursor between the two curves.
The calculator screen above shows that, for points to
the left of where the curves cross,
Y1
<
Y2
or
2
√
x
<
√
x
+
2
+
1. To solve the original inequality,
you must find points for which
Y1
>
Y2
. These are the
points to the right of where the curves cross.
Step 2
Use the
intersect
feature.
• You can use the
intersect
feature on the
CALC
menu
to approximate the
x
-coordinate of the point at
which the curves cross.
keystrokes
:
[CALC]
5
• Press
for each of
FIRST CURVE?
,
SECOND
CURVE?
, and
GUESS?
.
C07-034A-888482
[ 10, 10 ] scl: 1 by [ 10, 10] scl: 1
The calculator screen shows that the
x
-coordinate of
the point at which the curves cross is about 2.40.
Therefore, the solution of the inequality is about
x
>
2.40.
Use the symbol
>
in the solution because the
symbol in the original inequality is
>
.
Step 3
Use the
TABLE
feature to check your solution.
• Start the table at 2 and show
x
-values in increments
of 0.1. Scroll through the table.
keystrokes
:
[TBLSET]
2
.1
[TABLE]
Notice that when
x
is less than or equal to 2.4,
Y1
<
Y2
.
This verifies the solution
{
x
|
x
>
2.40
}
.
C07-035A-888482
Exercises
360
|
Extend 5-6
|
Graphing Technology Lab: Solving Radical Equations