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Check for Extraneous Solutions
4
EXAMPLE
Solve x
13 0 and check for extraneous solutions.
Solution
x
13 0
Write original equation.
x
13
2
(x
)
Subtract 13 from each side.
(13)2
x 169
ANSWER 䊳
Square each side.
Simplify.
169
13 0, so x 169 is not a solution. The equation has no
solution because x
≥ 0 for all values of x.
Check for Extraneous Solutions
Solve the equation. Check for extraneous solutions.
7. x
6 x
EXAMPLE
Science
8. x 8
2x
9. n
40
Use a Radical Model
5
The centripetal force F exerted on a passenger by a
spinning amusement park ride and the number of seconds t the ride takes to
complete one revolution are related by the following equation.
CENTRIPETAL FORCE
t
1620π
F
2
Find the centripetal force experienced by this person if t 10.
Solution
CENTRIPETAL FORCE
keeps you spinning in a circle
on an amusement park ride.
Forces can be measured
in newtons. A force of one
newton will accelerate a
mass of one kilogram at one
meter per second per second.
t
102 0π
162F
2
Write model for centripetal force.
2
Substitute 10 for t and square each side.
1620π2
F
Simplify.
1620π2
100
Solve for F.
1620π2
F
100 F ≈ 160
ANSWER 䊳
The person experiences a centripetal force of about 160 newtons.
Use a Radical Model
10. Find the centripetal force exerted on the passenger in Example 5 if the
amusement park ride takes 11 seconds to complete one revolution.
706
Chapter 12
Radicals and More Connections to Geometry