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secondary 3 | A Maths
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h + k + 2k = 2
h + 3k = 2
We take it as h and k are different.
The equation tells This tells you that some of those integers are non-positive
(If not , h + 3k would be bigger than 2. Eg. If k = 1 and h = 2)
h² + k² + (2k)² = 30
h² + k² + 4k² = 30
h² + 5k² = 30 ①
Since h + 3k = 2,
h = 2 - 3k
h² = (2 - 3k)²
h² = 4 - 12k + 9k² ②
Sub ② into ①,
4 - 12k + 9k² + 5k² = 30
14k² - 12k - 26 = 0
Divide both sides by 2,
7k² - 6k - 13 = 0
(7k - 13)(k + 1) = 0
7k = 13 or k = -1
k = -13/7
(Rejected as k is an integer)
So, k = -1 and 2k = -2
h = 2 - 3(1) = 5
Your integers are :
5 , -1 and -2
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