S3 Maths Inequalities?

用戶49050

2016-09-29 2:40 am

The difference between the squares of two positive consecutive even integers is not less than 36.Find the minimum value of the smaller even integer.

回答 (2)

SC147

2016-09-29 5:30 am

✔ 最佳答案

Let the 2 positive consecutive even integers = 2a, 2a+2
(2a+2)² - (2a)² ≧ 36
8a+4 ≧ 36
4(2a+1) ≧ 36
2a+1 ≧ 9
2a ≧ 8

∴ minimum value of the smaller even integer, 2a = 8

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Checking :-
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The 2 positive consecutive even integers = 8, 10
=> The difference between the squares of 2 positive consecutive even integers = 10² - 8² = 36,
which is the smallest no. "not less than 36" (題目的要求)！

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Hin Chung

2016-10-13 3:34 am

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