f.5 solving unknown

2012-05-22 2:06 am
the sum of the squares of two consecutive odd numbers is less then 100.find all possible values of the larger odd no.

ans. :3 ,5,7

回答 (1)

2012-05-22 6:37 am
✔ 最佳答案
Let n be the value of the smaller odd number.
Then, the larger odd number = n + 2

n² + (n + 2)² < 100
n² + n² + 4n + 4 < 100
2n² + 4n - 96 < 0
n² + 2n - 48 < 0
(n + 8)(n - 6) < 0
-8 < n < 6

Possible values of the smaller odd number : 1, 3, 5
Possible values of the larger odd number : 3, 5, 7

2012-05-23 21:28:18 補充:
If you have not given the answers, my answers should be :
......
......
-8 < n < 6
Possible values of the smaller odd number : -7, -5, -3, -1, 1, 3, 5
Possible values of the larger odd number : -5, -3, -1, 1, 3, 5, 7 ...... (answer)

2012-05-23 21:28:32 補充:
However, you answers only include positive odd numbers, so I think the word "positive" has been omitted or misspelt as "possible". Therefore, I neglected all negative odd numbers.
參考: micatkie, micatkie, micatkie


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