Arithmetik und Algebra: Aufgaben by L. Locher-Ernst

By L. Locher-Ernst

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1 4. 10. 5. b. 6. b. 7. -5' (6 a - b). 8. - 1. 9. 0. 10. (a b - c d): (a - b - c + d). 11. (as + a b + b2): (a + b + 1). 62 Lbsungen zu den Obungsaufgaben 12. (a l + a b + bl ): (1 - a - b). 13. 1 '3' 14. (at - a l + a l - b): al. 15. (b-a l -a·-a 4 ):a·. 17. 18. ~ + b). abc: (a + b + c). 20. (a l - bl ): (a 21. 10. ~. 22. 1. 19. (a+b):c. 23. 7. 24. ~ (a - b). 25. a. 26. 27. a + b. 28. (a - b)l. 29. c (a - b): (a + b). 1:4a(a+b). 31. a+b+c. 32. (bc-ad):(b+c-a-d). 33. 1: (b - a), (b - a): (a l - a b + 1), (a· - a b + 1): (- a' + a l b - 2 a + b).

5. x 9 + 2 x 8 + 7 X S + 8 x 4 + 3 x 3 + 4 x 2 + 3. 4. Gruppe 4. Die folgenden Ausdriicke sind nach Moglichkeit zu vereinfachen: (ab)C-(ba)C, (1"+P)C, (1+1")", (ab)"b, 2(1")b-(P)". 5. Die Zahl 21460 = (52 + 72) (11 2 + 132) a)s Summe zweier Quadrate zu schreiben. 1. Esistx=4ab(a 2 -b2), y=a 4 +b4 -6a2 b2, z=a 2 +b 2 • Wie gross wird a + z4 - (x 2 + y2) ? + (b - e - a) (e - a - b) + (e - a - b) (a - b - e) + (a 2 + b2 + e2 ) = d + 4)2 - (d - 3 c2 - 4)2 + (d - 4 + 3 e2)2 - (d + 4 - 3 e2)2 = ? 2. (a - b - e) (b - e - a) 3.

Abc: (a + b + c). 20. (a l - bl ): (a 21. 10. ~. 22. 1. 19. (a+b):c. 23. 7. 24. ~ (a - b). 25. a. 26. 27. a + b. 28. (a - b)l. 29. c (a - b): (a + b). 1:4a(a+b). 31. a+b+c. 32. (bc-ad):(b+c-a-d). 33. 1: (b - a), (b - a): (a l - a b + 1), (a· - a b + 1): (- a' + a l b - 2 a + b). 34. 1: (1 - a). 35. (a - 1): a. 36. a: (1 + 4 a). 37. a. 38. 25. 39. 7. 40. 5. 41. 20. 42. 15. 43. 5. 44. bl : a (b + 1)1. 45. 9. 46. 2 a. b e a 47. a + b, e - a, e - b. 48. a + b, a + b, a + b. 49. b' -c' a' 50. 0, a, b, e.

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