Math 125
Exam 5
Simplify. Rationalize, if appropriate. Assume all variables represent nonnegative values.
3
1) -216x4 y5
-6xy
2)
4
4
3
xy2
1536
4
6
3)
11x 3
·
12y5
4)
77x 8y9
=
7x 3y5
5)
3
3
3
112 ·
4
3
2 4 ·7 ·
3
3
3
24
2 2 ·7
4·7
28
4·3 - 4
2
7x 3y5 11x 5y4
=
7x 3y5
16
3
12 - 4
6)
33x 3y x 33xy
=
36y6
6y3
2 8 ·7
22
4
3y
=
3y
3 - 20
- 10
3
75 + 2
48
25·3 + 2
3 +8
3
16·3
11x 5y4 = x 2 y2
11x
7) 6 5 + 2 15 ( 15 - 2 55)
6 5 · 15 - 12 55 · 5 + 2 15 - 4 15 · 55
6 5 · 5 · 3 - 12 5 · 3 · 5 + 30 - 4 3 · 5 · 5 · 11
30
8) (5 +
3 - 60 11 + 30 - 20 33
3)2
25 + 10 3 + 3
28 + 10 3
9)
2 13 + 13 11 8 11 + 3 13
·
8 11 - 3 13 8 11 + 3 13
16 143 + 6 13 + 104 11 + 39 143
64 11 - 9 13
55 143 + 78 + 1144
704 - 117
55 143 + 78 + 1222
587
Solve. Check for extraneous solutions.
10) x 2 + 6x - 18 = 3
x2 + 6x - 18 = 9
x2 + 6x - 27 = 0
x+9 x-3 =0
x+9=0
x=- 9
- 9, 3
x-3=0
x=3
11) x =
x2 + 5x + 19 + 4
x - 4=
x 2 + 5x + 19
x2 - 8x + 16 = x 2 + 5x + 19
- 3 = 13x
x=-
12)
3
3
13
3
2x - 4 =
3x + 3
2x - 4 = 3x + 3
-7=x
-7
13)
x+ 6+
2-x=4
x+6 =4x + 62 = 4 -
2-x
2-x2
x + 6 = 16 - 8 2 - x + 2 - x
2x + 6 = 18 - 8 2 - x
2x - 12 = - 8 2 - x
x-6=-4 2-x
4 2-x=6-x
16 2 - x = 36 - 12x + x 2
32 - 16x = 36 - 12x + x 2
x 2 + 4x + 4 = 0
x+22=0
x+2=0
x=- 2
-2
Solve by completing the square.
14) x2 - 16x + 45 = 0
x2 - 16x = - 45
x2 - 16x + 64 = - 45 + 64
x - 8 2 = 19
x - 8 = ± 19
x = 8 ± 19
8 ± 19
15) x2 + 9x - 4 = 0
x2 + 9x = 4
x2 + 9x +
x+
x+
9 2 97
=
2
4
9
=±
2
97
2
9
±
2
97
2
x=-
x=
81 16 81
=
+
4
4
4
- 9 ± 97
2
- 9 ± 97
2