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Unformatted text preview: Solutions to Quiz 4A
www.math.uﬂ.edu/˜harringt
September 17, 2007
1. Reduce and simplify
√
(a) x2 + 4x + 4 = (x + 2)2 = x + 2 (b)
√
3 54 + √
3 12 + √
3 √
√
√
3
3
3
16 =
27 ∗ 2 + 22 ∗ 3 + 8 ∗ 2
√
√√
√√
3
3
3
3
3
=
27 2 + 22 ∗ 3 + 8 2
√
√
√
3
3
3
= 3 3 + 22 ∗ 3 + 2 2
√
√
√
3
3
3
=
3 3+2 2
22 ∗ 3
+
Combine like terms.
√
√
3
3
= 5 2 + 12 Does not reduce. (c)
x −1 + y −1
=
x
=
= 1
x + 1
y x
1
x
xy
x + 1
y x
+ xy
y xy
xy x2 y
y+x
=
x2 y
2. Determine validity of the following statements.
√
√
(a) ” x2 = ( x)2 for all real values of x.”
This statement is FALSE. Let x = −1. The right hand side is
not deﬁned while the left hand side is deﬁned.
1 √
√
3
(b) ” x3 = ( 3 x)3 for all real values of x.”
This statement is TRUE. Both sides are deﬁned and they are the
same for all values since the index is odd.
(c) ” x2 + y 2 = x + y for all positive values of x and y .”
This statement is FALSE. Let x = 1 and y = 1 and compute
both sides.
1 (d) ”4 2 = ±2.”
√
1
This statment is FALSE. 4 2 = 4 = 2. Here we are dealing with
the principle square root. So we only have one positive value. 2 ...
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 Fall '08
 WILLIAMSON
 Math, Calculus, Algebra

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