C H A P T E R 2 Polynomial and Rational Functions

186 Chapter 2 Polynomial and Rational Functions
89. False
i 44 i 150 i 74 i 109 i 61 i 4 11 i 4 37 i 2 i 4 18 i 2 i 4 27 i i 4 15 i
90. 66 6i6i 6i 2 6
91.
92.
1 11 1 37 1 1 18 1 1 27 i 1 15 i
1 1 1 i i 1
a 1 b 1ia 2 b 2i a 1a 2 a 1b 2i a 2b 1i b 1b 2i 2
a 1a 2 b 1b 2 a 1b 2 a 2b 1i
The complex conjugate of this product is a1a2 b1b2 a1b2 a2b1i. The product of the complex conjugates is:
a 1 b 1 ia 2 b 2 i a 1 a 2 a 1 b 2 i a 2 b 1 i b 1 b 2 i 2
a 1 a 2 b 1 b 2 a 1 b 2 a 2 b 1i
Thus, the complex conjugate of the product of two complex numbers is the product of their complex conjugates.
a 1 b 1i a 2 b 2i a 1 a 2 b 1 b 2i
The complex conjugate of this sum is a1 a2 b1 b2i. The sum of the complex conjugates is a1 b1i a2 b2i a1 a2 b1 b2i. Thus, the complex conjugate of the sum of two complex numbers is the sum of their complex conjugates.
93. 4 3x 8 6x x 2 x 2 3x 12
94. x3 3x2 6 2x 4x2 x3 3x2 6 2x 4x2 95. 3x 1
2x 4 3x2 12x 1
2x 2
4x 2 20x 25
x 3 x 2 2x 6
x 31
x 31
3x2 23
2 x 2
96. 2x 52 2x2 22x5 52 97. x 12 19 98. 8 3x 34
99. 45x 6 36x 1 0 100. 5x 3x 11 20x 15 101.
102.
20x 24 18x 3 0
r 2 m 1 m 2
F
2x 27 0
2x 27
x 27
2
r m1m2 F m1m2
F
F
F m1m2F F
5x 15x 55 20x 15
30x 40
x 40
30 4
3
3x 42
x 14
V 4
3 a2 b
3V 4a 2 b
3V
a2
4b
3V
a
4b
F m1m2 r2 103. Let x #
liters withdrawn and replaced.
0.505 x 1.00x 0.605
2.50 0.50x 1.00x 3.00
0.50x 0.50
x 1 liter
a 1
2 3V 3Vb
b 2b