quiz 4A sol - Solutions to Quiz 4A...

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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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quiz 4A sol - Solutions to Quiz 4A...

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