Geometry

# Download Affine Algebraic Geometry by Gutierrez J., Shpilrain V., Yu J.-T. (eds.) PDF

By Gutierrez J., Shpilrain V., Yu J.-T. (eds.)

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Example text

6 Ͻ Ϫ2, since Ϫ6 Ϫ ͑Ϫ2͒ ϭ Ϫ6 ϩ 2 ϭ Ϫ4 is negative. 33 ϭ 13 Ϫ 100 ϭ 300 is positive. 7 Ͼ 0, since 7 Ϫ 0 ϭ 7 is positive. Ϫ4 Ͻ 0, since Ϫ4 Ϫ 0 ϭ Ϫ4 is negative. The next law enables us to compare, or order, any two real numbers. If a and b are real numbers, then exactly one of the following is true: Trichotomy Law a ϭ b, TI-83/4 Plus Testing Inequalities and the Trichotomy Law a Ͼ b, or aϽb TI-86 5 2nd TEST 3 3 ENTER 5 2nd TEST > (F3) 3 ENTER 5 2nd TEST 5 3 ENTER 5 2nd TEST < (F2) 3 ENTER 5 2nd TEST 1 3 ENTER 5 2nd TEST == (F1) 3 ENTER The results indicate that “1” represents true and “0” represents false.

All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. 2, whenever an index of a radical is even (or a rational exponent m͞n with n even is employed), assume that the letters that appear in the radicand denote positive real numbers unless otherwise specified. 2 Exercises Exer. 1–10: Express the number in the form a͞b, where a and b are integers. 4 1 ͑ Ϫ 32 ͒ 2 ͑Ϫ3͒3 2Ϫ3 3 Ϫ2 3 20 ϩ 02 4 2ϩ0 5 Ϫ24 ϩ 3Ϫ1 6 ͑ Ϫ 23 ͒4 Ϫ 2Ϫ4 7 16Ϫ3/4 8 95/2 11 ͑ ͒͑16x ͒ 12 ͑Ϫ3x ͒͑4x ͒ 13 ͑2x 3͒͑3x 2͒ ͑x 2͒3 14 15 ͑ ͒͑Ϫ3a ͒͑4a ͒ Ϫ2 5 1 5 6a 2 7 35 ͑3x 5/6͒͑8x 2/3͒ 36 ͑8r͒1/3͑2r1/2͒ 37 ͑27a6͒Ϫ2/3 38 ͑25z4͒Ϫ3/2 39 ͑8xϪ2/3͒x1/6 40 ͑3x1/2͒͑Ϫ2x 5/2͒ 43 Exer.

11–46: Simplify. 008͒2/3 33 ͑4a3/2͒͑2a1/2͒ 45 4 ͩ ͪ ͩ ͪ Ϫ8x 3 yϪ6 x6 9yϪ4 2/3 42 Ϫ1/2 ͑x6y3͒Ϫ1/3 ͑x4y2͒Ϫ1/2 44 ͩ ͪ ͩ ͪ Ϫy3/2 yϪ1/3 3 cϪ4 16d 8 3/4 46 a4/3aϪ3/2a1/6 Exer. 47 – 52: Rewrite the expression using rational exponents. ͑2x 2͒3 4x 4 16 ͑Ϫ4b ͒͑ 3 1 2 6b ͒͑Ϫ9b ͒ 4 3 x 47 2 3 5 x 48 2 3 49 2 ͑a ϩ b͒2 50 ͙a ϩ 2b 3 3 52 2 r Ϫ s3 4 ͑6x 3͒2 и ͑3x 2͒0 17 ͑2x 2͒3 ͑3y 3͒͑2y 2͒2 и ͑ y 3͒0 18 ͑ y 4͒3 51 2x 2 ϩ y2 19 ͑3u7v3͒͑4u4vϪ5͒ 20 ͑x 2yz3͒͑Ϫ2xz 2͒͑x 3yϪ2͒ Exer. 53–56: Rewrite the expression using a radical.