Opener Solutions
#1
Chapter Seven—Section 7.7
Solving Equations
Containing Radicals
Opener Solutions
#2
1 = 1
3 27
92
1
1
b. 9 33 = 933 = 3 3 3
b
2 1
3
33 33
a.
f(g(x)) = 3x2-1
g(f(x)) = (3x-1)2 = 9x 2 - 6x+1
f(x) - g(x) = 3x - 1 - x2
f(x)g(x) = (3x - 1)(x2) = 3x3- x 2
g(x)
( ) = x2 ; x  1
3
f(x) 3x - 1
Opener Solutions
#3
a. 49  2 - 216  2  7 2 - 8 2  - 2
2 5 1
b. 2  5  1 
 5 1
4
2
5-1 5  1
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Opener Solutions
#4
.98.5 h
.98
98  h
.5
2
2
.98  h
.5
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Opener Solutions
#5
a. x+2)(x+3  0
x = -2, -3
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b. (4x + 1)(5x - 3) = 0
x = -1 , 3
4 5
2
.98  h
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h
3.8
3 8 feet
#1 Solve:
x + 13 - 8 = - 2
add 8
x+13 = 6
square both sides
x+13 = 36
subtract 13
x = 23
#1 Check:
#2 Solve:
23 + 13 - 8 = - 2
36 = 6
x-8+5=7
subtract 5
x-8=2
square both sides
6=6
x-8=4
This is true so, the
final answer is 23
23.
add 8
x = 12
#2 Check:
12 - 8 + 5 = 7
4+5=7
2+5=7
7=7
This is true. Therefore, 12 is
the final solution.
Do 3, 4, 5, 6, and 7 with your group.
#3 y = 5
#8 Solve:
A questions???
Any
ti
???
#4 t = 6
add x + 35 to isolate one radical
#5 y = 3
x + 8 = - 3 + x + 35
Do you need to see
any work???
k???
#6 t = 40
square both
b th sides
id
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#7 y = 1
#8 Solve:
x+8
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= - 3 + x + 35
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2
#8 Solve:
x+8 = 9 - 6 x + 35 + x + 35
square both sides
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x + 8 - x + 35 = - 3
x+8
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= -3 + x + 35 -3 + x + 35
F.O.I.L.
x+8 = 9 - 6 x + 35 + x + 35
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subtract x, 9, and 35 from both sides
then divide by -6 to isolate x + 35
8-9-35 = x + 35
6
-6
square both sides and solve for x
#8 Solve:
#8 Check:
Square both sides and solve for x.
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2
8-9-35 = x + 35
6
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2
36 = x+35
9 - 36 = - 3
3 - 6 = -3
3
-33 = -33
x=1
This is true so 1 is the solution.
#9 Solve:
#9 Solve:
x + 8 - 1 = x+2
one radical
di l is
i already
l d isolated
i l d
so square both sides
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1 + 8 - 1 + 35 = - 3
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2
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x + 8 - 1 = xx+22
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2
x+8-1 =
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x+8-1
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x+2
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x+8-1 
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F.O.I.L.
x+8-2 x+8+1=x+2
x+2
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2
#9 Solve:
x+8-2 x+8+1=x+2
Subtract
S
b
x, 88, and
d 1 ffrom bboth
h sides
id off the
h equation
i
then divide by -2 to isolate the radical x + 8.
x + 8 = 2 -8 -1
-22
Then square both sides and solve for x.
#9 Check:
#9 Solve:
Then square both sides
and solve for x.
x
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2 2 -8 -1 2
x+8 =
-2
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x + 8 = 49
4
x = 49 - 8
4
x = 17
4
17 + 8 - 1 = 17 + 2
4
4
17 + 32 - 1 = 17 + 8
4 4
4
4
49 - 1 = 25
4
4
7- 2= 5
2 2 2
5=5
2 2
So 17 is the solution
So,
solution.
4
Do #10 and #11 with your group.
#10 x = 249
64
#11
l = 1.82 feet
See the screen for
the work when you
are finished with
your quizzes.
Homework:
P
Pg.
456
1,5,7,11,23,25,26,33,34,37,39,
41,43,49,13,35,65
(d iin thi
(do
this order)
d )
Only 17 problems 
See board for test date.