Question

Please answer question 10 will rate brainliest answer

Answer 1

Answer:

n^2/8

4^2/8

16/8

2

2 is the right answer

Answer 2

Answer:

Sol: If 'n' is an odd positive integer, show that (n2-1) Is divisible by 8?? Any odd positive integer is in the form of 4p + 1 or 4p+ 3 for some integer p. Let n = 4p+ 1, (n2 – 1) = (4p + 1)2 – 1 = 16p2 + 8p + 1 = 16p2 + 8p = 8p (2p + 1) ⇒ (n2 – 1) is divisible by 8. (n2 – 1) = (4p + 3)2 – 1 = 16p2 + 24p + 9 – 1 = 16p2 + 24p + 8 = 8(2p2 + 3p + 1) ⇒ n2– 1 is divisible by 8. Therefore, n2– 1 is divisible by 8 if n is an odd positive integer.

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Answer 3

Answer:

Any odd positive integer n can be written in form of 4q + 1 or 4q + 3.

If n = 4q + 1, when n² - 1 = (4q + 1)2 - 1 = 16q2 + 8q + 1 - 1 = 8q(2q + 1) which is divisible by 8.

If n = 4q + 3, when n² - 1 = (4q + 3)2 - 1 = 16q² + 24q + 9 - 1 = 8(2q²+ 3q + 1) which is divisible by 8.

So, it is clear that n2 - 1 is divisible by 8, if n is an odd positive integer.

Step-by-step explanation:

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