Question

Questions :-
6. Explain the comparison Cpazia 3)
a) Some boys
B) THeir not studying
C) yet passing in the test​

Answer 1

Answer:

a

Explanation:

a answer is correcting

Answer 2

Answer:

1. Let us consider a positive integer a
3. Divide the positive integer a by 3, and let r be the reminder and b be the quotient such that
5. a = 3b + r……………………………(1)
7. where r = 0,1,2,3…..
9. Case 1: Consider r = 0
11. Equation (1) becomes
13. a = 3b
15. On squaring both the side
17. a2 = (3b)2
19. a2 = 9b2
21. a2 = 3 × 3b2
23. a2 = 3m
25. Where m = 3b2
27. Case 2: Let r = 1
29. Equation (1) becomes
31. a = 3b + 1
33. Squaring on both the side we get
35. a2 = (3b + 1)2
37. a2 = (3b)2 + 1 + 2 × (3b) × 1
39. a2 = 9b2 + 6b + 1
41. a2 = 3(3b2 + 2b) + 1
43. a2 = 3m + 1
45. Where m = 3b2 + 2b
47. Case 3: Let r = 2
49. Equation (1) becomes
51. a = 3b + 2
53. Squaring on both the sides we get
55. a2 = (3b + 2)2
57. a2 = 9b2 + 4 + (2 × 3b × 2)
59. a2 = 9b2 + 12b + 3 + 1
61. a2 = 3(3b2 + 4b + 1) + 1
63. a2 = 3m + 1
65. where m = 3b2 + 4b + 1
67. ∴ square of any positive integer is of the form 3m or 3m+1.
69. Hence proved.