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New SAT Math Workbook Episode 1 part 8

Tham khảo tài liệu 'new sat math workbook episode 1 part 8', ngoại ngữ, ngữ pháp tiếng anh phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Concepts of Algebra Signed Numbers and Equations 125 5. EQUATIONS CONTAINING RADICALS In solving equations containing radicals it is important to get the radical alone on one side of the equation. Then square both sides to eliminate the radical sign. Solve the resulting equation. Remember that all solutions to radical equations must be checked as squaring both sides may sometimes result in extraneous roots. In squaring each side of an equation do not make the mistake of simply squaring each term. The entire side of the equation must be multiplied by itself. Example Jx-3 4 Solution x - 3 16 x 19 Checking we have -716 4 which is true. Example 77-3 -4 Solution x - 3 16 x 19 Checking we have -716 -4 which is not true since the radical sign means the principal or positive square root only. is 4 not -4 therefore this equation has no solution. Example 7x2 - 7 1 x Solution First get the radical alone on one side then square. Vx2 - 7 x - 1 x2 - 7 x2 - 2x 1 - 7 - 2x 1 2x 8 x 4 Checking we have -79 1 4 3 1 4 which is true. www.petersons.com 126 Chapter 8 Exercise 5 Work out each problem. Circle the letter that appears before your answer. 1. Solve for y yỊĩỹ 11 15 A 4 B 2 C 8 D 1 E no solution 2. Solve for x 4y 2x -1 12 A 18.5 B 4 C 10 D 5 E no solution 3. Solve for x Jx2 - 35 5 - x A 6 B -6 C 3 D -3 E no solution 4. Solve for y 26 3 yỊĩỹ 8 A 6 B 18 C 3 D -6 E no solution 5. Solve for x 4 A 10 B 20 C 30 D 40 E no solution www.petersons.com Concepts of Algebra Signed Numbers and Equations 127 RETEST Work out each problem. Circle the letter that appears before your answer. 1. When -5 is subtracted from the sum of -3 and 6. Solve for x 3x 2y 5a b 7 the result is 4x - 3y a 7b A 15 A a b B -1 C -9 D 9 E 1 c 1Ì c 1Ì B a - b C 2a b D 17a 17b E 4a - 6b 7. Solve for x 8x2 7x 6x 4x2 2. The product of 1 - 2 1 -4 12 1 - 61 is A 2 B -2 C 4 D -4 E -12 3. When the sum of -4 and -5 is divided by the A -1 B 0 and 1 4 C 0 D 0 and -1 product of 9 and - 27 the result is A -3 B 3 C -27 D 27 E -3 .